LMFDB - Embedded newform 570.2.k.a.533.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(77,570)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("570.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			533.10
Character	$\chi$	$=$	570.533
Dual form			570.2.k.a.77.10

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-1.55987 - 0.752859i) q^{3} +1.00000i q^{4} +(-1.50962 + 1.64956i) q^{5} +(-0.570645 - 1.63535i) q^{6} +(0.306664 - 0.306664i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.86641 + 2.34873i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-1.55987 - 0.752859i) q^{3} +1.00000i q^{4} +(-1.50962 + 1.64956i) q^{5} +(-0.570645 - 1.63535i) q^{6} +(0.306664 - 0.306664i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.86641 + 2.34873i) q^{9} +(-2.23388 + 0.0989549i) q^{10} +0.944248i q^{11} +(0.752859 - 1.55987i) q^{12} +(-4.86057 - 4.86057i) q^{13} +0.433689 q^{14} +(3.59670 - 1.43658i) q^{15} -1.00000 q^{16} +(-2.18295 - 2.18295i) q^{17} +(-0.341054 + 2.98055i) q^{18} -1.00000i q^{19} +(-1.64956 - 1.50962i) q^{20} +(-0.709233 + 0.247482i) q^{21} +(-0.667684 + 0.667684i) q^{22} +(-5.00219 + 5.00219i) q^{23} +(1.63535 - 0.570645i) q^{24} +(-0.442106 - 4.98042i) q^{25} -6.87388i q^{26} +(-1.14309 - 5.06886i) q^{27} +(0.306664 + 0.306664i) q^{28} +1.77850 q^{29} +(3.55906 + 1.52744i) q^{30} -10.9563 q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.710886 - 1.47291i) q^{33} -3.08715i q^{34} +(0.0429156 + 0.968808i) q^{35} +(-2.34873 + 1.86641i) q^{36} +(-3.09818 + 3.09818i) q^{37} +(0.707107 - 0.707107i) q^{38} +(3.92254 + 11.2412i) q^{39} +(-0.0989549 - 2.23388i) q^{40} -6.08532i q^{41} +(-0.676500 - 0.326507i) q^{42} +(-3.19643 - 3.19643i) q^{43} -0.944248 q^{44} +(-6.69193 - 0.466933i) q^{45} -7.07416 q^{46} +(4.22008 + 4.22008i) q^{47} +(1.55987 + 0.752859i) q^{48} +6.81191i q^{49} +(3.20907 - 3.83430i) q^{50} +(1.76167 + 5.04857i) q^{51} +(4.86057 - 4.86057i) q^{52} +(5.08232 - 5.08232i) q^{53} +(2.77594 - 4.39251i) q^{54} +(-1.55759 - 1.42545i) q^{55} +0.433689i q^{56} +(-0.752859 + 1.55987i) q^{57} +(1.25759 + 1.25759i) q^{58} -7.52893 q^{59} +(1.43658 + 3.59670i) q^{60} +4.53489 q^{61} +(-7.74725 - 7.74725i) q^{62} +(1.29263 + 0.147911i) q^{63} -1.00000i q^{64} +(15.3554 - 0.680204i) q^{65} +(1.54417 - 0.538830i) q^{66} +(7.65067 - 7.65067i) q^{67} +(2.18295 - 2.18295i) q^{68} +(11.5687 - 4.03683i) q^{69} +(-0.654705 + 0.715397i) q^{70} +12.9834i q^{71} +(-2.98055 - 0.341054i) q^{72} +(2.53764 + 2.53764i) q^{73} -4.38149 q^{74} +(-3.05992 + 8.10166i) q^{75} +1.00000 q^{76} +(0.289567 + 0.289567i) q^{77} +(-5.17507 + 10.7224i) q^{78} +9.50297i q^{79} +(1.50962 - 1.64956i) q^{80} +(-2.03306 + 8.76736i) q^{81} +(4.30297 - 4.30297i) q^{82} +(-7.84806 + 7.84806i) q^{83} +(-0.247482 - 0.709233i) q^{84} +(6.89632 - 0.305489i) q^{85} -4.52043i q^{86} +(-2.77424 - 1.33896i) q^{87} +(-0.667684 - 0.667684i) q^{88} +8.88554 q^{89} +(-4.40174 - 5.06208i) q^{90} -2.98113 q^{91} +(-5.00219 - 5.00219i) q^{92} +(17.0904 + 8.24852i) q^{93} +5.96810i q^{94} +(1.64956 + 1.50962i) q^{95} +(0.570645 + 1.63535i) q^{96} +(-0.722973 + 0.722973i) q^{97} +(-4.81675 + 4.81675i) q^{98} +(-2.21778 + 1.76235i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7}+O(q^{10}) $ 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7	$ 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} - 32 q^{21} - 4 q^{22} + 32 q^{25} + 28 q^{27} - 12 q^{28} - 8 q^{30} + 8 q^{31} + 36 q^{33} + 4 q^{36} - 32 q^{37} - 8 q^{40} + 12 q^{42} - 24 q^{43} - 28 q^{45} - 16 q^{46} - 4 q^{48} - 40 q^{51} - 8 q^{52} - 4 q^{55} + 4 q^{57} - 4 q^{58} - 24 q^{60} + 200 q^{61} + 28 q^{63} + 12 q^{70} - 68 q^{73} - 36 q^{75} + 36 q^{76} + 24 q^{78} - 92 q^{81} + 24 q^{82} + 24 q^{85} + 28 q^{87} - 4 q^{88} - 68 q^{90} + 64 q^{91} + 16 q^{93} - 4 q^{96} - 148 q^{97}+O(q^{100}) $ 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7 - 4 * q^10 - 4 * q^12 + 8 * q^13 + 4 * q^15 - 36 * q^16 - 32 * q^21 - 4 * q^22 + 32 * q^25 + 28 * q^27 - 12 * q^28 - 8 * q^30 + 8 * q^31 + 36 * q^33 + 4 * q^36 - 32 * q^37 - 8 * q^40 + 12 * q^42 - 24 * q^43 - 28 * q^45 - 16 * q^46 - 4 * q^48 - 40 * q^51 - 8 * q^52 - 4 * q^55 + 4 * q^57 - 4 * q^58 - 24 * q^60 + 200 * q^61 + 28 * q^63 + 12 * q^70 - 68 * q^73 - 36 * q^75 + 36 * q^76 + 24 * q^78 - 92 * q^81 + 24 * q^82 + 24 * q^85 + 28 * q^87 - 4 * q^88 - 68 * q^90 + 64 * q^91 + 16 * q^93 - 4 * q^96 - 148 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	−1.55987	−	0.752859i	−0.900593	−	0.434663i
$3$	−1.55987	−	0.752859i	−0.900593	−	0.434663i
$4$			1.00000i			0.500000i
$5$	−1.50962	+	1.64956i	−0.675122	+	0.737706i
$5$	−1.50962	+	1.64956i	−0.675122	+	0.737706i
$6$	−0.570645	−	1.63535i	−0.232965	−	0.667628i
$7$	0.306664	−	0.306664i	0.115908	−	0.115908i	−0.646774	−	0.762682i	$-0.723882\pi$
$7$	0.306664	−	0.306664i	0.115908	−	0.115908i	0.762682	+	0.646774i	$0.223882\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	1.86641	+	2.34873i	0.622135	+	0.782910i
$10$	−2.23388	+	0.0989549i	−0.706414	+	0.0312923i
$11$			0.944248i			0.284701i	0.989816	+	0.142351i	$0.0454661\pi$
$11$			0.944248i			0.284701i	−0.989816	+	0.142351i	$0.954534\pi$
$12$	0.752859	−	1.55987i	0.217332	−	0.450296i
$13$	−4.86057	−	4.86057i	−1.34808	−	1.34808i	−0.887747	−	0.460332i	$-0.847730\pi$
$13$	−4.86057	−	4.86057i	−1.34808	−	1.34808i	−0.460332	−	0.887747i	$-0.652270\pi$
$14$	0.433689			0.115908
$15$	3.59670	−	1.43658i	0.928664	−	0.370922i
$16$	−1.00000			−0.250000
$17$	−2.18295	−	2.18295i	−0.529443	−	0.529443i	0.390964	−	0.920406i	$-0.372142\pi$
$17$	−2.18295	−	2.18295i	−0.529443	−	0.529443i	−0.920406	+	0.390964i	$0.872142\pi$
$18$	−0.341054	+	2.98055i	−0.0803872	+	0.702523i
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	−1.64956	−	1.50962i	−0.368853	−	0.337561i
$21$	−0.709233	+	0.247482i	−0.154767	+	0.0540051i
$22$	−0.667684	+	0.667684i	−0.142351	+	0.142351i
$23$	−5.00219	+	5.00219i	−1.04303	+	1.04303i	−0.0439961	+	0.999032i	$0.514009\pi$
$23$	−5.00219	+	5.00219i	−1.04303	+	1.04303i	−0.999032	+	0.0439961i	$0.985991\pi$
$24$	1.63535	−	0.570645i	0.333814	−	0.116482i
$25$	−0.442106	−	4.98042i	−0.0884212	−	0.996083i
$26$		−	6.87388i		−	1.34808i
$27$	−1.14309	−	5.06886i	−0.219988	−	0.975502i
$28$	0.306664	+	0.306664i	0.0579541	+	0.0579541i
$29$	1.77850			0.330260			0.165130	−	0.986272i	$-0.447196\pi$
$29$	1.77850			0.330260			0.165130	+	0.986272i	$0.447196\pi$
$30$	3.55906	+	1.52744i	0.649793	+	0.278871i
$31$	−10.9563			−1.96780			−0.983901	−	0.178714i	$-0.942806\pi$
$31$	−10.9563			−1.96780			−0.983901	+	0.178714i	$0.942806\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	0.710886	−	1.47291i	0.123749	−	0.256400i
$34$		−	3.08715i		−	0.529443i
$35$	0.0429156	+	0.968808i	0.00725407	+	0.163758i
$36$	−2.34873	+	1.86641i	−0.391455	+	0.311068i
$37$	−3.09818	+	3.09818i	−0.509338	+	0.509338i	−0.914323	−	0.404985i	$-0.867277\pi$
$37$	−3.09818	+	3.09818i	−0.509338	+	0.509338i	0.404985	+	0.914323i	$0.367277\pi$
$38$	0.707107	−	0.707107i	0.114708	−	0.114708i
$39$	3.92254	+	11.2412i	0.628110	+	1.80003i
$40$	−0.0989549	−	2.23388i	−0.0156461	−	0.353207i
$41$		−	6.08532i		−	0.950368i	−0.879886	−	0.475184i	$-0.842382\pi$
$41$		−	6.08532i		−	0.950368i	0.879886	−	0.475184i	$-0.157618\pi$
$42$	−0.676500	−	0.326507i	−0.104386	−	0.0503811i
$43$	−3.19643	−	3.19643i	−0.487451	−	0.487451i	0.420050	−	0.907501i	$-0.362013\pi$
$43$	−3.19643	−	3.19643i	−0.487451	−	0.487451i	−0.907501	+	0.420050i	$0.862013\pi$
$44$	−0.944248			−0.142351
$45$	−6.69193	−	0.466933i	−0.997575	−	0.0696062i
$46$	−7.07416			−1.04303
$47$	4.22008	+	4.22008i	0.615562	+	0.615562i	0.944390	−	0.328828i	$-0.106654\pi$
$47$	4.22008	+	4.22008i	0.615562	+	0.615562i	−0.328828	+	0.944390i	$0.606654\pi$
$48$	1.55987	+	0.752859i	0.225148	+	0.108666i
$49$			6.81191i			0.973131i
$50$	3.20907	−	3.83430i	0.453831	−	0.542252i
$51$	1.76167	+	5.04857i	0.246683	+	0.706942i
$52$	4.86057	−	4.86057i	0.674040	−	0.674040i
$53$	5.08232	−	5.08232i	0.698110	−	0.698110i	−0.265893	−	0.964003i	$-0.585667\pi$
$53$	5.08232	−	5.08232i	0.698110	−	0.698110i	0.964003	+	0.265893i	$0.0856667\pi$
$54$	2.77594	−	4.39251i	0.377757	−	0.597745i
$55$	−1.55759	−	1.42545i	−0.210026	−	0.192208i
$56$			0.433689i			0.0579541i
$57$	−0.752859	+	1.55987i	−0.0997186	+	0.206610i
$58$	1.25759	+	1.25759i	0.165130	+	0.165130i
$59$	−7.52893			−0.980183			−0.490092	−	0.871671i	$-0.663037\pi$
$59$	−7.52893			−0.980183			−0.490092	+	0.871671i	$0.663037\pi$
$60$	1.43658	+	3.59670i	0.185461	+	0.464332i
$61$	4.53489			0.580633			0.290316	−	0.956931i	$-0.406239\pi$
$61$	4.53489			0.580633			0.290316	+	0.956931i	$0.406239\pi$
$62$	−7.74725	−	7.74725i	−0.983901	−	0.983901i
$63$	1.29263	+	0.147911i	0.162856	+	0.0186351i
$64$		−	1.00000i		−	0.125000i
$65$	15.3554	−	0.680204i	1.90460	−	0.0843689i
$66$	1.54417	−	0.538830i	0.190075	−	0.0663254i
$67$	7.65067	−	7.65067i	0.934678	−	0.934678i	−0.0633153	−	0.997994i	$-0.520167\pi$
$67$	7.65067	−	7.65067i	0.934678	−	0.934678i	0.997994	+	0.0633153i	$0.0201674\pi$
$68$	2.18295	−	2.18295i	0.264721	−	0.264721i
$69$	11.5687	−	4.03683i	1.39271	−	0.485977i
$70$	−0.654705	+	0.715397i	−0.0782522	+	0.0855062i
$71$			12.9834i			1.54085i	0.637531	+	0.770425i	$0.279956\pi$
$71$			12.9834i			1.54085i	−0.637531	+	0.770425i	$0.720044\pi$
$72$	−2.98055	−	0.341054i	−0.351261	−	0.0401936i
$73$	2.53764	+	2.53764i	0.297009	+	0.297009i	0.839841	−	0.542832i	$-0.182648\pi$
$73$	2.53764	+	2.53764i	0.297009	+	0.297009i	−0.542832	+	0.839841i	$0.682648\pi$
$74$	−4.38149			−0.509338
$75$	−3.05992	+	8.10166i	−0.353329	+	0.935499i
$76$	1.00000			0.114708
$77$	0.289567	+	0.289567i	0.0329992	+	0.0329992i
$78$	−5.17507	+	10.7224i	−0.585961	+	1.21407i
$79$			9.50297i			1.06917i	0.845115	+	0.534584i	$0.179532\pi$
$79$			9.50297i			1.06917i	−0.845115	+	0.534584i	$0.820468\pi$
$80$	1.50962	−	1.64956i	0.168780	−	0.184427i
$81$	−2.03306	+	8.76736i	−0.225895	+	0.974152i
$82$	4.30297	−	4.30297i	0.475184	−	0.475184i
$83$	−7.84806	+	7.84806i	−0.861436	+	0.861436i	−0.991505	−	0.130069i	$-0.958480\pi$
$83$	−7.84806	+	7.84806i	−0.861436	+	0.861436i	0.130069	+	0.991505i	$0.458480\pi$
$84$	−0.247482	−	0.709233i	−0.0270025	−	0.0773836i
$85$	6.89632	−	0.305489i	0.748011	−	0.0331349i
$86$		−	4.52043i		−	0.487451i
$87$	−2.77424	−	1.33896i	−0.297430	−	0.143552i
$88$	−0.667684	−	0.667684i	−0.0711753	−	0.0711753i
$89$	8.88554			0.941866			0.470933	−	0.882169i	$-0.343917\pi$
$89$	8.88554			0.941866			0.470933	+	0.882169i	$0.343917\pi$
$90$	−4.40174	−	5.06208i	−0.463984	−	0.533590i
$91$	−2.98113			−0.312507
$92$	−5.00219	−	5.00219i	−0.521514	−	0.521514i
$93$	17.0904	+	8.24852i	1.77219	+	0.855332i
$94$			5.96810i			0.615562i
$95$	1.64956	+	1.50962i	0.169241	+	0.154884i
$96$	0.570645	+	1.63535i	0.0582412	+	0.166907i
$97$	−0.722973	+	0.722973i	−0.0734067	+	0.0734067i	−0.742857	−	0.669450i	$-0.766530\pi$
$97$	−0.722973	+	0.722973i	−0.0734067	+	0.0734067i	0.669450	+	0.742857i	$0.266530\pi$
$98$	−4.81675	+	4.81675i	−0.486565	+	0.486565i
$99$	−2.21778	+	1.76235i	−0.222895	+	0.177123i
$100$	4.98042	−	0.442106i	0.498042	−	0.0442106i
$101$		−	1.65814i		−	0.164991i	−0.996591	−	0.0824956i	$-0.973711\pi$
$101$		−	1.65814i		−	0.164991i	0.996591	−	0.0824956i	$-0.0262890\pi$
$102$	−2.32419	+	4.81557i	−0.230129	+	0.476812i
$103$	−1.69267	−	1.69267i	−0.166784	−	0.166784i	0.618780	−	0.785564i	$-0.287627\pi$
$103$	−1.69267	−	1.69267i	−0.166784	−	0.166784i	−0.785564	+	0.618780i	$0.787627\pi$
$104$	6.87388			0.674040
$105$	0.662433	−	1.54353i	0.0646468	−	0.150633i
$106$	7.18748			0.698110
$107$	−7.42775	−	7.42775i	−0.718067	−	0.718067i	0.250142	−	0.968209i	$-0.419523\pi$
$107$	−7.42775	−	7.42775i	−0.718067	−	0.718067i	−0.968209	+	0.250142i	$0.919523\pi$
$108$	5.06886	−	1.14309i	0.487751	−	0.109994i
$109$		−	7.49186i		−	0.717590i	−0.933416	−	0.358795i	$-0.883188\pi$
$109$		−	7.49186i		−	0.717590i	0.933416	−	0.358795i	$-0.116812\pi$
$110$	−0.0934379	−	2.10933i	−0.00890895	−	0.201117i
$111$	7.16526	−	2.50027i	0.680097	−	0.237315i
$112$	−0.306664	+	0.306664i	−0.0289771	+	0.0289771i
$113$	−11.8230	+	11.8230i	−1.11222	+	1.11222i	−0.119367	+	0.992850i	$0.538087\pi$
$113$	−11.8230	+	11.8230i	−1.11222	+	1.11222i	−0.992850	+	0.119367i	$0.961913\pi$
$114$	−1.63535	+	0.570645i	−0.153164	+	0.0534458i
$115$	−0.700022	−	15.8028i	−0.0652774	−	1.47362i
$116$			1.77850i			0.165130i
$117$	2.34436	−	20.4880i	0.216737	−	1.89411i
$118$	−5.32376	−	5.32376i	−0.490092	−	0.490092i
$119$	−1.33886			−0.122734
$120$	−1.52744	+	3.55906i	−0.139435	+	0.324897i
$121$	10.1084			0.918945
$122$	3.20665	+	3.20665i	0.290316	+	0.290316i
$123$	−4.58139	+	9.49233i	−0.413090	+	0.855895i
$124$		−	10.9563i		−	0.983901i
$125$	8.88291	+	6.78925i	0.794512	+	0.607249i
$126$	0.809440	+	1.01862i	0.0721106	+	0.0907457i
$127$	1.42736	−	1.42736i	0.126658	−	0.126658i	−0.640936	−	0.767594i	$-0.721454\pi$
$127$	1.42736	−	1.42736i	0.126658	−	0.126658i	0.767594	+	0.640936i	$0.221454\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	2.57956	+	7.39249i	0.227118	+	0.650872i
$130$	11.3389	+	10.3769i	0.994486	+	0.910117i
$131$			18.5477i			1.62052i	0.586073	+	0.810258i	$0.300673\pi$
$131$			18.5477i			1.62052i	−0.586073	+	0.810258i	$0.699327\pi$
$132$	1.47291	+	0.710886i	0.128200	+	0.0618746i
$133$	−0.306664	−	0.306664i	−0.0265912	−	0.0265912i
$134$	10.8197			0.934678
$135$	10.0870	+	5.76644i	0.868153	+	0.496296i
$136$	3.08715			0.264721
$137$	−2.22249	−	2.22249i	−0.189880	−	0.189880i	0.605764	−	0.795644i	$-0.292868\pi$
$137$	−2.22249	−	2.22249i	−0.189880	−	0.189880i	−0.795644	+	0.605764i	$0.792868\pi$
$138$	11.0348	+	5.32585i	0.939343	+	0.453366i
$139$		−	18.9629i		−	1.60841i	−0.594350	−	0.804206i	$-0.702591\pi$
$139$		−	18.9629i		−	1.60841i	0.594350	−	0.804206i	$-0.297409\pi$
$140$	−0.968808	+	0.0429156i	−0.0818792	+	0.00362703i
$141$	−3.40566	−	9.75992i	−0.286809	−	0.821933i
$142$	−9.18067	+	9.18067i	−0.770425	+	0.770425i
$143$	4.58958	−	4.58958i	0.383800	−	0.383800i
$144$	−1.86641	−	2.34873i	−0.155534	−	0.195727i
$145$	−2.68486	+	2.93375i	−0.222966	+	0.243635i
$146$			3.58877i			0.297009i
$147$	5.12841	−	10.6257i	0.422984	−	0.876395i
$148$	−3.09818	−	3.09818i	−0.254669	−	0.254669i
$149$	−12.9585			−1.06160			−0.530799	−	0.847498i	$-0.678108\pi$
$149$	−12.9585			−1.06160			−0.530799	+	0.847498i	$0.678108\pi$
$150$	−7.89243	+	3.56505i	−0.644414	+	0.291085i
$151$	4.35166			0.354133			0.177067	−	0.984199i	$-0.443339\pi$
$151$	4.35166			0.354133			0.177067	+	0.984199i	$0.443339\pi$
$152$	0.707107	+	0.707107i	0.0573539	+	0.0573539i
$153$	1.05289	−	9.20142i	0.0851208	−	0.743891i
$154$			0.409510i			0.0329992i
$155$	16.5398	−	18.0730i	1.32851	−	1.45166i
$156$	−11.2412	+	3.92254i	−0.900016	+	0.314055i
$157$	−5.26086	+	5.26086i	−0.419863	+	0.419863i	−0.885156	−	0.465294i	$-0.845949\pi$
$157$	−5.26086	+	5.26086i	−0.419863	+	0.419863i	0.465294	+	0.885156i	$0.345949\pi$
$158$	−6.71962	+	6.71962i	−0.534584	+	0.534584i
$159$	−11.7540	+	4.10150i	−0.932156	+	0.325270i
$160$	2.23388	−	0.0989549i	0.176604	−	0.00782307i
$161$			3.06798i			0.241791i
$162$	−7.63705	+	4.76187i	−0.600023	+	0.374128i
$163$	−2.53089	−	2.53089i	−0.198234	−	0.198234i	0.601008	−	0.799243i	$-0.294766\pi$
$163$	−2.53089	−	2.53089i	−0.198234	−	0.198234i	−0.799243	+	0.601008i	$0.794766\pi$
$164$	6.08532			0.475184
$165$	1.35648	+	3.39618i	0.105602	+	0.264392i
$166$	−11.0988			−0.861436
$167$	3.33084	+	3.33084i	0.257749	+	0.257749i	0.824138	−	0.566389i	$-0.191660\pi$
$167$	3.33084	+	3.33084i	0.257749	+	0.257749i	−0.566389	+	0.824138i	$0.691660\pi$
$168$	0.326507	−	0.676500i	0.0251905	−	0.0521931i
$169$			34.2502i			2.63463i
$170$	5.09245	+	4.66042i	0.390573	+	0.357438i
$171$	2.34873	−	1.86641i	0.179612	−	0.142728i
$172$	3.19643	−	3.19643i	0.243725	−	0.243725i
$173$	−9.61343	+	9.61343i	−0.730896	+	0.730896i	−0.970797	−	0.239902i	$-0.922885\pi$
$173$	−9.61343	+	9.61343i	−0.730896	+	0.730896i	0.239902	+	0.970797i	$0.422885\pi$
$174$	−1.01489	−	2.90847i	−0.0769389	−	0.220491i
$175$	−1.66289	−	1.39174i	−0.125703	−	0.105206i
$176$		−	0.944248i		−	0.0711753i
$177$	11.7442	+	5.66823i	0.882746	+	0.426050i
$178$	6.28303	+	6.28303i	0.470933	+	0.470933i
$179$	−22.6680			−1.69429			−0.847143	−	0.531365i	$-0.821679\pi$
$179$	−22.6680			−1.69429			−0.847143	+	0.531365i	$0.821679\pi$
$180$	0.466933	−	6.69193i	0.0348031	−	0.498787i
$181$	3.95190			0.293743			0.146871	−	0.989156i	$-0.453080\pi$
$181$	3.95190			0.293743			0.146871	+	0.989156i	$0.453080\pi$
$182$	−2.10797	−	2.10797i	−0.156253	−	0.156253i
$183$	−7.07384	−	3.41413i	−0.522914	−	0.252380i
$184$		−	7.07416i		−	0.521514i
$185$	−0.433570	−	9.78771i	−0.0318767	−	0.719607i
$186$	6.25213	+	17.9173i	0.458429	+	1.31376i
$187$	2.06124	−	2.06124i	0.150733	−	0.150733i
$188$	−4.22008	+	4.22008i	−0.307781	+	0.307781i
$189$	−1.90498	−	1.20389i	−0.138567	−	0.0875703i
$190$	0.0989549	+	2.23388i	0.00717894	+	0.162062i
$191$			3.21978i			0.232975i	0.993192	+	0.116487i	$0.0371635\pi$
$191$			3.21978i			0.232975i	−0.993192	+	0.116487i	$0.962837\pi$
$192$	−0.752859	+	1.55987i	−0.0543329	+	0.112574i
$193$	−8.96414	−	8.96414i	−0.645253	−	0.645253i	0.306589	−	0.951842i	$-0.400812\pi$
$193$	−8.96414	−	8.96414i	−0.645253	−	0.645253i	−0.951842	+	0.306589i	$0.900812\pi$
$194$	−1.02244			−0.0734067
$195$	−24.4646	−	10.4994i	−1.75194	−	0.751880i
$196$	−6.81191			−0.486565
$197$	−6.36112	−	6.36112i	−0.453211	−	0.453211i	0.443208	−	0.896419i	$-0.353840\pi$
$197$	−6.36112	−	6.36112i	−0.453211	−	0.453211i	−0.896419	+	0.443208i	$0.853840\pi$
$198$	−2.81438	−	0.322039i	−0.200009	−	0.0228863i
$199$			21.5251i			1.52588i	0.646472	+	0.762938i	$0.276244\pi$
$199$			21.5251i			1.52588i	−0.646472	+	0.762938i	$0.723756\pi$
$200$	3.83430	+	3.20907i	0.271126	+	0.226915i
$201$	−17.6940	+	6.17419i	−1.24804	+	0.435494i
$202$	1.17248	−	1.17248i	0.0824956	−	0.0824956i
$203$	0.545404	−	0.545404i	0.0382798	−	0.0382798i
$204$	−5.04857	+	1.76167i	−0.353471	+	0.123341i
$205$	10.0381	+	9.18652i	0.701092	+	0.641614i
$206$		−	2.39380i		−	0.166784i
$207$	−21.0849	−	2.41267i	−1.46550	−	0.167692i
$208$	4.86057	+	4.86057i	0.337020	+	0.337020i
$209$	0.944248			0.0653150
$210$	1.55985	−	0.623027i	0.107640	−	0.0429930i
$211$	−1.03406			−0.0711877			−0.0355938	−	0.999366i	$-0.511332\pi$
$211$	−1.03406			−0.0711877			−0.0355938	+	0.999366i	$0.511332\pi$
$212$	5.08232	+	5.08232i	0.349055	+	0.349055i
$213$	9.77470	−	20.2525i	0.669751	−	1.38768i
$214$		−	10.5044i		−	0.718067i
$215$	10.0981	−	0.447319i	0.688684	−	0.0305069i
$216$	4.39251	+	2.77594i	0.298873	+	0.188879i
$217$	−3.35989	+	3.35989i	−0.228085	+	0.228085i
$218$	5.29755	−	5.29755i	0.358795	−	0.358795i
$219$	−2.04791	−	5.86889i	−0.138385	−	0.396583i
$220$	1.42545	−	1.55759i	0.0961040	−	0.105013i
$221$			21.2207i			1.42746i
$222$	6.83457	+	3.29864i	0.458706	+	0.221391i
$223$	−4.32004	−	4.32004i	−0.289291	−	0.289291i	0.547509	−	0.836800i	$-0.315576\pi$
$223$	−4.32004	−	4.32004i	−0.289291	−	0.289291i	−0.836800	+	0.547509i	$0.815576\pi$
$224$	−0.433689			−0.0289771
$225$	10.8725	−	10.3339i	0.724833	−	0.688924i
$226$	−16.7203			−1.11222
$227$	8.83516	+	8.83516i	0.586410	+	0.586410i	0.936657	−	0.350247i	$-0.113902\pi$
$227$	8.83516	+	8.83516i	0.586410	+	0.586410i	−0.350247	+	0.936657i	$0.613902\pi$
$228$	−1.55987	−	0.752859i	−0.103305	−	0.0498593i
$229$		−	21.6673i		−	1.43182i	−0.698194	−	0.715908i	$-0.746013\pi$
$229$		−	21.6673i		−	1.43182i	0.698194	−	0.715908i	$-0.253987\pi$
$230$	10.6793	−	11.6693i	0.704171	−	0.769448i
$231$	−0.233685	−	0.669691i	−0.0153753	−	0.0440624i
$232$	−1.25759	+	1.25759i	−0.0825649	+	0.0825649i
$233$	10.5947	−	10.5947i	0.694079	−	0.694079i	−0.269048	−	0.963127i	$-0.586709\pi$
$233$	10.5947	−	10.5947i	0.694079	−	0.694079i	0.963127	+	0.269048i	$0.0867089\pi$
$234$	16.1449	−	12.8295i	1.05542	−	0.838688i
$235$	−13.3320	+	0.590572i	−0.869683	+	0.0385247i
$236$		−	7.52893i		−	0.490092i
$237$	7.15440	−	14.8234i	0.464728	−	0.962885i
$238$	−0.946720	−	0.946720i	−0.0613668	−	0.0613668i
$239$	−11.6073			−0.750812			−0.375406	−	0.926860i	$-0.622497\pi$
$239$	−11.6073			−0.750812			−0.375406	+	0.926860i	$0.622497\pi$
$240$	−3.59670	+	1.43658i	−0.232166	+	0.0927306i
$241$	20.6897			1.33274			0.666369	−	0.745622i	$-0.267848\pi$
$241$	20.6897			1.33274			0.666369	+	0.745622i	$0.267848\pi$
$242$	7.14772	+	7.14772i	0.459473	+	0.459473i
$243$	9.77190	−	12.1454i	0.626868	−	0.779126i
$244$			4.53489i			0.290316i
$245$	−11.2367	−	10.2834i	−0.717885	−	0.656982i
$246$	−9.95162	+	3.47256i	−0.634492	+	0.221402i
$247$	−4.86057	+	4.86057i	−0.309271	+	0.309271i
$248$	7.74725	−	7.74725i	0.491951	−	0.491951i
$249$	18.1505	−	6.33349i	1.15024	−	0.401369i
$250$	1.48045	+	11.0819i	0.0936317	+	0.700880i
$251$		−	15.5598i		−	0.982128i	−0.871123	−	0.491064i	$-0.836608\pi$
$251$		−	15.5598i		−	0.982128i	0.871123	−	0.491064i	$-0.163392\pi$
$252$	−0.147911	+	1.29263i	−0.00931754	+	0.0814282i
$253$	−4.72330	−	4.72330i	−0.296951	−	0.296951i
$254$	2.01860			0.126658
$255$	−10.9874	−	4.71544i	−0.688056	−	0.295292i
$256$	1.00000			0.0625000
$257$	2.98574	+	2.98574i	0.186245	+	0.186245i	0.794071	−	0.607825i	$-0.207958\pi$
$257$	2.98574	+	2.98574i	0.186245	+	0.186245i	−0.607825	+	0.794071i	$0.707958\pi$
$258$	−3.40325	+	7.05130i	−0.211877	+	0.438995i
$259$			1.90020i			0.118073i
$260$	0.680204	+	15.3554i	0.0421845	+	0.952302i
$261$	3.31941	+	4.17722i	0.205466	+	0.258564i
$262$	−13.1152	+	13.1152i	−0.810258	+	0.810258i
$263$	−8.55701	+	8.55701i	−0.527648	+	0.527648i	−0.919870	−	0.392222i	$-0.871706\pi$
$263$	−8.55701	+	8.55701i	−0.527648	+	0.527648i	0.392222	+	0.919870i	$0.371706\pi$
$264$	0.538830	+	1.54417i	0.0331627	+	0.0950373i
$265$	0.711236	+	16.0560i	0.0436909	+	0.986309i
$266$		−	0.433689i		−	0.0265912i
$267$	−13.8603	−	6.68956i	−0.848237	−	0.409395i
$268$	7.65067	+	7.65067i	0.467339	+	0.467339i
$269$	−11.0350			−0.672814			−0.336407	−	0.941717i	$-0.609212\pi$
$269$	−11.0350			−0.672814			−0.336407	+	0.941717i	$0.609212\pi$
$270$	3.05512	+	11.2101i	0.185929	+	0.682225i
$271$	−12.1851			−0.740190			−0.370095	−	0.928994i	$-0.620675\pi$
$271$	−12.1851			−0.740190			−0.370095	+	0.928994i	$0.620675\pi$
$272$	2.18295	+	2.18295i	0.132361	+	0.132361i
$273$	4.65018	+	2.24437i	0.281442	+	0.135835i
$274$		−	3.14308i		−	0.189880i
$275$	4.70275	−	0.417458i	0.283586	−	0.0251736i
$276$	4.03683	+	11.5687i	0.242989	+	0.696355i
$277$	4.80867	−	4.80867i	0.288925	−	0.288925i	−0.547730	−	0.836655i	$-0.684508\pi$
$277$	4.80867	−	4.80867i	0.288925	−	0.288925i	0.836655	+	0.547730i	$0.184508\pi$
$278$	13.4088	−	13.4088i	0.804206	−	0.804206i
$279$	−20.4488	−	25.7333i	−1.22424	−	1.54061i
$280$	−0.715397	−	0.654705i	−0.0427531	−	0.0391261i
$281$		−	32.0631i		−	1.91273i	−0.292180	−	0.956363i	$-0.594381\pi$
$281$		−	32.0631i		−	1.91273i	0.292180	−	0.956363i	$-0.405619\pi$
$282$	4.49314	−	9.30947i	0.267562	−	0.554371i
$283$	8.65468	+	8.65468i	0.514467	+	0.514467i	0.915892	−	0.401425i	$-0.131485\pi$
$283$	8.65468	+	8.65468i	0.514467	+	0.514467i	−0.401425	+	0.915892i	$0.631485\pi$
$284$	−12.9834			−0.770425
$285$	−1.43658	−	3.59670i	−0.0850954	−	0.213050i
$286$	6.49065			0.383800
$287$	−1.86615	−	1.86615i	−0.110155	−	0.110155i
$288$	0.341054	−	2.98055i	0.0200968	−	0.175631i
$289$		−	7.46948i		−	0.439381i
$290$	−3.97296	+	0.175992i	−0.233300	+	0.0103346i
$291$	1.67204	−	0.583449i	0.0980168	−	0.0342024i
$292$	−2.53764	+	2.53764i	−0.148504	+	0.148504i
$293$	7.19596	−	7.19596i	0.420392	−	0.420392i	−0.464947	−	0.885339i	$-0.653926\pi$
$293$	7.19596	−	7.19596i	0.420392	−	0.420392i	0.885339	+	0.464947i	$0.153926\pi$
$294$	11.1399	−	3.88718i	0.649689	−	0.226705i
$295$	11.3658	−	12.4194i	0.661743	−	0.723087i
$296$		−	4.38149i		−	0.254669i
$297$	4.78626	−	1.07936i	0.277727	−	0.0626310i
$298$	−9.16302	−	9.16302i	−0.530799	−	0.530799i
$299$	48.6269			2.81217
$300$	−8.10166	−	3.05992i	−0.467749	−	0.176665i
$301$	−1.96046			−0.112999
$302$	3.07709	+	3.07709i	0.177067	+	0.177067i
$303$	−1.24835	+	2.58649i	−0.0717156	+	0.148590i
$304$			1.00000i			0.0573539i
$305$	−6.84595	+	7.48057i	−0.391998	+	0.428336i
$306$	7.25089	−	5.76188i	0.414506	−	0.329385i
$307$	−1.61182	+	1.61182i	−0.0919916	+	0.0919916i	−0.751605	−	0.659613i	$-0.770720\pi$
$307$	−1.61182	+	1.61182i	−0.0919916	+	0.0919916i	0.659613	+	0.751605i	$0.270720\pi$
$308$	−0.289567	+	0.289567i	−0.0164996	+	0.0164996i
$309$	1.36601	+	3.91469i	0.0777094	+	0.222699i
$310$	24.4749	−	1.08418i	1.39008	−	0.0615770i
$311$		−	24.1698i		−	1.37055i	−0.728286	−	0.685273i	$-0.759683\pi$
$311$		−	24.1698i		−	1.37055i	0.728286	−	0.685273i	$-0.240317\pi$
$312$	−10.7224	−	5.17507i	−0.607035	−	0.292980i
$313$	−20.5330	−	20.5330i	−1.16059	−	1.16059i	−0.984346	−	0.176245i	$-0.943605\pi$
$313$	−20.5330	−	20.5330i	−1.16059	−	1.16059i	−0.176245	−	0.984346i	$-0.556395\pi$
$314$	−7.43999			−0.419863
$315$	−2.19537	+	1.90899i	−0.123695	+	0.107559i
$316$	−9.50297			−0.534584
$317$	18.3162	+	18.3162i	1.02874	+	1.02874i	0.999575	+	0.0291663i	$0.00928523\pi$
$317$	18.3162	+	18.3162i	1.02874	+	1.02874i	0.0291663	+	0.999575i	$0.490715\pi$
$318$	−11.2116	−	5.41116i	−0.628713	−	0.303443i
$319$			1.67935i			0.0940254i
$320$	1.64956	+	1.50962i	0.0922133	+	0.0843902i
$321$	5.99429	+	17.1784i	0.334569	+	0.958804i
$322$	−2.16939	+	2.16939i	−0.120896	+	0.120896i
$323$	−2.18295	+	2.18295i	−0.121462	+	0.121462i
$324$	−8.76736	−	2.03306i	−0.487076	−	0.112948i
$325$	−22.0588	+	26.3565i	−1.22360	+	1.46200i
$326$		−	3.57921i		−	0.198234i
$327$	−5.64032	+	11.6864i	−0.311910	+	0.646257i
$328$	4.30297	+	4.30297i	0.237592	+	0.237592i
$329$	2.58830			0.142697
$330$	−1.44228	+	3.36064i	−0.0793949	+	0.184997i
$331$	16.5637			0.910424			0.455212	−	0.890383i	$-0.349563\pi$
$331$	16.5637			0.910424			0.455212	+	0.890383i	$0.349563\pi$
$332$	−7.84806	−	7.84806i	−0.430718	−	0.430718i
$333$	−13.0593	−	1.49432i	−0.715643	−	0.0818885i
$334$			4.71053i			0.257749i
$335$	1.07066	+	24.1698i	0.0584964	+	1.32054i
$336$	0.709233	−	0.247482i	0.0386918	−	0.0135013i
$337$	25.3948	−	25.3948i	1.38334	−	1.38334i	0.544735	−	0.838608i	$-0.316630\pi$
$337$	25.3948	−	25.3948i	1.38334	−	1.38334i	0.838608	−	0.544735i	$-0.183370\pi$
$338$	−24.2186	+	24.2186i	−1.31732	+	1.31732i
$339$	27.3435	−	9.54135i	1.48510	−	0.518215i
$340$	0.305489	+	6.89632i	0.0165675	+	0.374006i
$341$		−	10.3454i		−	0.560236i
$342$	2.98055	+	0.341054i	0.161170	+	0.0184421i
$343$	4.23562	+	4.23562i	0.228702	+	0.228702i
$344$	4.52043			0.243725
$345$	−10.8053	+	25.1774i	−0.581740	+	1.35550i
$346$	−13.5954			−0.730896
$347$	−5.68399	−	5.68399i	−0.305133	−	0.305133i	0.537885	−	0.843018i	$-0.319223\pi$
$347$	−5.68399	−	5.68399i	−0.305133	−	0.305133i	−0.843018	+	0.537885i	$0.819223\pi$
$348$	1.33896	−	2.77424i	0.0717759	−	0.148715i
$349$			18.1493i			0.971512i	0.874094	+	0.485756i	$0.161456\pi$
$349$			18.1493i			0.971512i	−0.874094	+	0.485756i	$0.838544\pi$
$350$	−0.191737	−	2.15995i	−0.0102487	−	0.115454i
$351$	−19.0815	+	30.1936i	−1.01849	+	1.61162i
$352$	0.667684	−	0.667684i	0.0355877	−	0.0355877i
$353$	8.86486	−	8.86486i	0.471829	−	0.471829i	−0.430677	−	0.902506i	$-0.641725\pi$
$353$	8.86486	−	8.86486i	0.471829	−	0.471829i	0.902506	+	0.430677i	$0.141725\pi$
$354$	4.29635	+	12.3124i	0.228348	+	0.654398i
$355$	−21.4170	−	19.6000i	−1.13669	−	1.04026i
$356$			8.88554i			0.470933i
$357$	2.08846	+	1.00798i	0.110533	+	0.0533478i
$358$	−16.0287	−	16.0287i	−0.847143	−	0.847143i
$359$	10.7838			0.569150			0.284575	−	0.958654i	$-0.408148\pi$
$359$	10.7838			0.569150			0.284575	+	0.958654i	$0.408148\pi$
$360$	5.06208	−	4.40174i	0.266795	−	0.231992i
$361$	−1.00000			−0.0526316
$362$	2.79442	+	2.79442i	0.146871	+	0.146871i
$363$	−15.7678	−	7.61020i	−0.827596	−	0.399432i
$364$		−	2.98113i		−	0.156253i
$365$	−8.01687	+	0.355126i	−0.419622	+	0.0185882i
$366$	−2.58781	−	7.41612i	−0.135267	−	0.387647i
$367$	−9.27545	+	9.27545i	−0.484175	+	0.484175i	−0.906462	−	0.422287i	$-0.861227\pi$
$367$	−9.27545	+	9.27545i	−0.484175	+	0.484175i	0.422287	+	0.906462i	$0.361227\pi$
$368$	5.00219	−	5.00219i	0.260757	−	0.260757i
$369$	14.2928	−	11.3577i	0.744052	−	0.591257i
$370$	6.61438	−	7.22754i	0.343865	−	0.375742i
$371$		−	3.11713i		−	0.161833i
$372$	−8.24852	+	17.0904i	−0.427666	+	0.886094i
$373$	−4.66943	−	4.66943i	−0.241774	−	0.241774i	0.575810	−	0.817584i	$-0.304687\pi$
$373$	−4.66943	−	4.66943i	−0.241774	−	0.241774i	−0.817584	+	0.575810i	$0.804687\pi$
$374$	2.91504			0.150733
$375$	−8.74487	−	17.2779i	−0.451583	−	0.892229i
$376$	−5.96810			−0.307781
$377$	−8.64454	−	8.64454i	−0.445216	−	0.445216i
$378$	−0.495747	−	2.19831i	−0.0254985	−	0.113069i
$379$			21.6246i			1.11078i	0.831590	+	0.555390i	$0.187431\pi$
$379$			21.6246i			1.11078i	−0.831590	+	0.555390i	$0.812569\pi$
$380$	−1.50962	+	1.64956i	−0.0774418	+	0.0846207i
$381$	−3.30111	+	1.15190i	−0.169121	+	0.0590138i
$382$	−2.27673	+	2.27673i	−0.116487	+	0.116487i
$383$	−19.8243	+	19.8243i	−1.01297	+	1.01297i	−0.0130600	+	0.999915i	$0.504157\pi$
$383$	−19.8243	+	19.8243i	−1.01297	+	1.01297i	−0.999915	+	0.0130600i	$0.995843\pi$
$384$	−1.63535	+	0.570645i	−0.0834535	+	0.0291206i
$385$	−0.914795	+	0.0405230i	−0.0466222	+	0.00206524i
$386$		−	12.6772i		−	0.645253i
$387$	1.54171	−	13.4734i	0.0783696	−	0.684891i
$388$	−0.722973	−	0.722973i	−0.0367034	−	0.0367034i
$389$	−18.0320			−0.914258			−0.457129	−	0.889400i	$-0.651122\pi$
$389$	−18.0320			−0.914258			−0.457129	+	0.889400i	$0.651122\pi$
$390$	−9.87485	−	24.7233i	−0.500033	−	1.25191i
$391$	21.8390			1.10445
$392$	−4.81675	−	4.81675i	−0.243283	−	0.243283i
$393$	13.9638	−	28.9320i	0.704379	−	1.45943i
$394$		−	8.99598i		−	0.453211i
$395$	−15.6757	−	14.3459i	−0.788732	−	0.721819i
$396$	−1.76235	−	2.21778i	−0.0885614	−	0.111448i
$397$	−15.1322	+	15.1322i	−0.759462	+	0.759462i	−0.976224	−	0.216763i	$-0.930450\pi$
$397$	−15.1322	+	15.1322i	−0.759462	+	0.759462i	0.216763	+	0.976224i	$0.430450\pi$
$398$	−15.2206	+	15.2206i	−0.762938	+	0.762938i
$399$	0.247482	+	0.709233i	0.0123896	+	0.0355060i
$400$	0.442106	+	4.98042i	0.0221053	+	0.249021i
$401$		−	10.1310i		−	0.505916i	−0.967477	−	0.252958i	$-0.918597\pi$
$401$		−	10.1310i		−	0.505916i	0.967477	−	0.252958i	$-0.0814034\pi$
$402$	−16.8773	−	8.14570i	−0.841765	−	0.406270i
$403$	53.2536	+	53.2536i	2.65275	+	2.65275i
$404$	1.65814			0.0824956
$405$	−11.3932	−	16.5890i	−0.566131	−	0.824315i
$406$	0.771317			0.0382798
$407$	−2.92545	−	2.92545i	−0.145009	−	0.145009i
$408$	−4.81557	−	2.32419i	−0.238406	−	0.115065i
$409$			8.93136i			0.441627i	0.975316	+	0.220814i	$0.0708713\pi$
$409$			8.93136i			0.441627i	−0.975316	+	0.220814i	$0.929129\pi$
$410$	0.602172	+	13.5939i	0.0297392	+	0.671353i
$411$	1.79358	+	5.14003i	0.0884709	+	0.253539i
$412$	1.69267	−	1.69267i	0.0833918	−	0.0833918i
$413$	−2.30886	+	2.30886i	−0.113611	+	0.113611i
$414$	−13.2033	−	16.6153i	−0.648904	−	0.816597i
$415$	−1.09828	−	24.7934i	−0.0539126	−	1.21706i
$416$			6.87388i			0.337020i
$417$	−14.2764	+	29.5797i	−0.699118	+	1.44853i
$418$	0.667684	+	0.667684i	0.0326575	+	0.0326575i
$419$	−20.6060			−1.00667			−0.503333	−	0.864092i	$-0.667893\pi$
$419$	−20.6060			−1.00667			−0.503333	+	0.864092i	$0.667893\pi$
$420$	1.54353	+	0.662433i	0.0753164	+	0.0323234i
$421$	15.1039			0.736120			0.368060	−	0.929802i	$-0.380022\pi$
$421$	15.1039			0.736120			0.368060	+	0.929802i	$0.380022\pi$
$422$	−0.731191	−	0.731191i	−0.0355938	−	0.0355938i
$423$	−2.03544	+	17.7882i	−0.0989666	+	0.864892i
$424$			7.18748i			0.349055i
$425$	−9.90689	+	11.8371i	−0.480555	+	0.574183i
$426$	21.2324	−	7.40893i	1.02871	−	0.358964i
$427$	1.39069	−	1.39069i	0.0673001	−	0.0673001i
$428$	7.42775	−	7.42775i	0.359034	−	0.359034i
$429$	−10.6145	+	3.70385i	−0.512471	+	0.178824i
$430$	7.45673	+	6.82413i	0.359596	+	0.329089i
$431$		−	7.39471i		−	0.356191i	−0.984013	−	0.178095i	$-0.943006\pi$
$431$		−	7.39471i		−	0.356191i	0.984013	−	0.178095i	$-0.0569936\pi$
$432$	1.14309	+	5.06886i	0.0549971	+	0.243876i
$433$	−6.52218	−	6.52218i	−0.313436	−	0.313436i	0.532803	−	0.846239i	$-0.321139\pi$
$433$	−6.52218	−	6.52218i	−0.313436	−	0.313436i	−0.846239	+	0.532803i	$0.821139\pi$
$434$	−4.75161			−0.228085
$435$	6.39674	−	2.55495i	0.306700	−	0.122501i
$436$	7.49186			0.358795
$437$	5.00219	+	5.00219i	0.239287	+	0.239287i
$438$	2.70184	−	5.59802i	0.129099	−	0.267484i
$439$		−	32.0835i		−	1.53126i	−0.643279	−	0.765632i	$-0.722426\pi$
$439$		−	32.0835i		−	1.53126i	0.643279	−	0.765632i	$-0.277574\pi$
$440$	2.10933	−	0.0934379i	0.100559	−	0.00445448i
$441$	−15.9993	+	12.7138i	−0.761873	+	0.605419i
$442$	−15.0053	+	15.0053i	−0.713730	+	0.713730i
$443$	−5.56755	+	5.56755i	−0.264522	+	0.264522i	−0.826888	−	0.562366i	$-0.809891\pi$
$443$	−5.56755	+	5.56755i	−0.264522	+	0.264522i	0.562366	+	0.826888i	$0.309891\pi$
$444$	2.50027	+	7.16526i	0.118658	+	0.340048i
$445$	−13.4138	+	14.6572i	−0.635874	+	0.694820i
$446$		−	6.10946i		−	0.289291i
$447$	20.2136	+	9.75590i	0.956068	+	0.461438i
$448$	−0.306664	−	0.306664i	−0.0144885	−	0.0144885i
$449$	−22.1426			−1.04497			−0.522487	−	0.852647i	$-0.674996\pi$
$449$	−22.1426			−1.04497			−0.522487	+	0.852647i	$0.674996\pi$
$450$	14.9952	+	0.380871i	0.706879	+	0.0179544i
$451$	5.74605			0.270571
$452$	−11.8230	−	11.8230i	−0.556109	−	0.556109i
$453$	−6.78804	−	3.27619i	−0.318930	−	0.153929i
$454$			12.4948i			0.586410i
$455$	4.50036	−	4.91755i	0.210980	−	0.230538i
$456$	−0.570645	−	1.63535i	−0.0267229	−	0.0765822i
$457$	1.27154	−	1.27154i	0.0594803	−	0.0594803i	−0.676741	−	0.736221i	$-0.736608\pi$
$457$	1.27154	−	1.27154i	0.0594803	−	0.0594803i	0.736221	+	0.676741i	$0.236608\pi$
$458$	15.3211	−	15.3211i	0.715908	−	0.715908i
$459$	−8.56974	+	13.5604i	−0.400001	+	0.632944i
$460$	15.8028	−	0.700022i	0.736809	−	0.0326387i
$461$		−	31.2805i		−	1.45688i	−0.685111	−	0.728439i	$-0.740246\pi$
$461$		−	31.2805i		−	1.45688i	0.685111	−	0.728439i	$-0.259754\pi$
$462$	0.308303	−	0.638783i	0.0143436	−	0.0297189i
$463$	12.3092	+	12.3092i	0.572056	+	0.572056i	0.932702	−	0.360647i	$-0.117444\pi$
$463$	12.3092	+	12.3092i	0.572056	+	0.572056i	−0.360647	+	0.932702i	$0.617444\pi$
$464$	−1.77850			−0.0825649
$465$	−39.4064	+	15.7395i	−1.82743	+	0.729902i
$466$	14.9831			0.694079
$467$	3.08706	+	3.08706i	0.142852	+	0.142852i	0.774916	−	0.632064i	$-0.217792\pi$
$467$	3.08706	+	3.08706i	0.142852	+	0.142852i	−0.632064	+	0.774916i	$0.717792\pi$
$468$	20.4880	+	2.34436i	0.947056	+	0.108368i
$469$		−	4.69238i		−	0.216674i
$470$	−9.84474	−	9.00955i	−0.454104	−	0.415579i
$471$	12.1670	−	4.24559i	0.560624	−	0.195626i
$472$	5.32376	−	5.32376i	0.245046	−	0.245046i
$473$	3.01822	−	3.01822i	0.138778	−	0.138778i
$474$	15.5407	−	5.42282i	0.713807	−	0.249078i
$475$	−4.98042	+	0.442106i	−0.228517	+	0.0202852i
$476$		−	1.33886i		−	0.0613668i
$477$	21.4227	+	2.45132i	0.980876	+	0.112238i
$478$	−8.20758	−	8.20758i	−0.375406	−	0.375406i
$479$	3.14915			0.143888			0.0719441	−	0.997409i	$-0.477080\pi$
$479$	3.14915			0.143888			0.0719441	+	0.997409i	$0.477080\pi$
$480$	−3.55906	−	1.52744i	−0.162448	−	0.0697177i
$481$	30.1178			1.37326
$482$	14.6298	+	14.6298i	0.666369	+	0.666369i
$483$	2.30976	−	4.78567i	0.105098	−	0.217755i
$484$			10.1084i			0.459473i
$485$	−0.101175	−	2.28400i	−0.00459413	−	0.103711i
$486$	15.4978	−	1.67829i	0.702997	−	0.0761289i
$487$	−14.2900	+	14.2900i	−0.647541	+	0.647541i	−0.952398	−	0.304857i	$-0.901391\pi$
$487$	−14.2900	+	14.2900i	−0.647541	+	0.647541i	0.304857	+	0.952398i	$0.401391\pi$
$488$	−3.20665	+	3.20665i	−0.145158	+	0.145158i
$489$	2.04246	+	5.85326i	0.0923632	+	0.264694i
$490$	−0.674072	−	15.2170i	−0.0304515	−	0.687433i
$491$			3.56231i			0.160765i	0.996764	+	0.0803823i	$0.0256141\pi$
$491$			3.56231i			0.160765i	−0.996764	+	0.0803823i	$0.974386\pi$
$492$	−9.49233	−	4.58139i	−0.427947	−	0.206545i
$493$	−3.88238	−	3.88238i	−0.174854	−	0.174854i
$494$	−6.87388			−0.309271
$495$	0.440900	−	6.31884i	0.0198170	−	0.284011i
$496$	10.9563			0.491951
$497$	3.98156	+	3.98156i	0.178597	+	0.178597i
$498$	17.3128	+	8.35586i	0.775804	+	0.374435i
$499$			22.7927i			1.02034i	0.860074	+	0.510170i	$0.170417\pi$
$499$			22.7927i			1.02034i	−0.860074	+	0.510170i	$0.829583\pi$
$500$	−6.78925	+	8.88291i	−0.303624	+	0.397256i
$501$	−2.68804	−	7.70335i	−0.120093	−	0.344160i
$502$	11.0025	−	11.0025i	0.491064	−	0.491064i
$503$	−2.87058	+	2.87058i	−0.127993	+	0.127993i	−0.768201	−	0.640208i	$-0.778848\pi$
$503$	−2.87058	+	2.87058i	−0.127993	+	0.127993i	0.640208	+	0.768201i	$0.278848\pi$
$504$	−1.01862	+	0.809440i	−0.0453728	+	0.0360553i
$505$	2.73521	+	2.50316i	0.121715	+	0.111389i
$506$		−	6.67976i		−	0.296951i
$507$	25.7856	−	53.4260i	1.14518	−	2.37273i
$508$	1.42736	+	1.42736i	0.0633291	+	0.0633291i
$509$	12.2215			0.541709			0.270854	−	0.962620i	$-0.412694\pi$
$509$	12.2215			0.541709			0.270854	+	0.962620i	$0.412694\pi$
$510$	−4.43493	−	11.1036i	−0.196382	−	0.491674i
$511$	1.55641			0.0688515
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−5.06886	+	1.14309i	−0.223796	+	0.0504688i
$514$			4.22247i			0.186245i
$515$	5.34745	−	0.236878i	0.235637	−	0.0104381i
$516$	−7.39249	+	2.57956i	−0.325436	+	0.113559i
$517$	−3.98480	+	3.98480i	−0.175251	+	0.175251i
$518$	−1.34365	+	1.34365i	−0.0590365	+	0.0590365i
$519$	22.2333	−	7.75817i	0.975933	−	0.340546i
$520$	−10.3769	+	11.3389i	−0.455059	+	0.497243i
$521$			41.4157i			1.81446i	0.420639	+	0.907228i	$0.361806\pi$
$521$			41.4157i			1.81446i	−0.420639	+	0.907228i	$0.638194\pi$
$522$	−0.606566	+	5.30092i	−0.0265487	+	0.232015i
$523$	−0.411090	−	0.411090i	−0.0179757	−	0.0179757i	0.698062	−	0.716038i	$-0.254046\pi$
$523$	−0.411090	−	0.411090i	−0.0179757	−	0.0179757i	−0.716038	+	0.698062i	$0.754046\pi$
$524$	−18.5477			−0.810258
$525$	1.54612	+	3.42286i	0.0674782	+	0.149386i
$526$	−12.1014			−0.527648
$527$	23.9169	+	23.9169i	1.04184	+	1.04184i
$528$	−0.710886	+	1.47291i	−0.0309373	+	0.0641000i
$529$		−	27.0437i		−	1.17581i
$530$	−10.8504	+	11.8562i	−0.471309	+	0.515000i
$531$	−14.0520	−	17.6834i	−0.609807	−	0.767395i
$532$	0.306664	−	0.306664i	0.0132956	−	0.0132956i
$533$	−29.5781	+	29.5781i	−1.28117	+	1.28117i
$534$	−5.07049	−	14.5310i	−0.219421	−	0.628816i
$535$	23.4656	−	1.03946i	1.01451	−	0.0449399i
$536$			10.8197i			0.467339i
$537$	35.3592	+	17.0658i	1.52586	+	0.736444i
$538$	−7.80290	−	7.80290i	−0.336407	−	0.336407i
$539$	−6.43213			−0.277052
$540$	−5.76644	+	10.0870i	−0.248148	+	0.434077i
$541$	−0.975280			−0.0419306			−0.0209653	−	0.999780i	$-0.506674\pi$
$541$	−0.975280			−0.0419306			−0.0209653	+	0.999780i	$0.506674\pi$
$542$	−8.61614	−	8.61614i	−0.370095	−	0.370095i
$543$	−6.16447	−	2.97523i	−0.264543	−	0.127679i
$544$			3.08715i			0.132361i
$545$	12.3583	+	11.3099i	0.529371	+	0.484461i
$546$	1.70116	+	4.87518i	0.0728031	+	0.208638i
$547$	−8.86543	+	8.86543i	−0.379058	+	0.379058i	−0.870762	−	0.491704i	$-0.836374\pi$
$547$	−8.86543	+	8.86543i	−0.379058	+	0.379058i	0.491704	+	0.870762i	$0.336374\pi$
$548$	2.22249	−	2.22249i	0.0949402	−	0.0949402i
$549$	8.46394	+	10.6512i	0.361232	+	0.454583i
$550$	3.62053	+	3.03016i	0.154380	+	0.129206i
$551$		−	1.77850i		−	0.0757668i
$552$	−5.32585	+	11.0348i	−0.226683	+	0.469672i
$553$	2.91422	+	2.91422i	0.123925	+	0.123925i
$554$	6.80049			0.288925
$555$	−6.69245	+	15.5940i	−0.284079	+	0.661928i
$556$	18.9629			0.804206
$557$	18.8971	+	18.8971i	0.800694	+	0.800694i	0.983204	−	0.182510i	$-0.0584222\pi$
$557$	18.8971	+	18.8971i	0.800694	+	0.800694i	−0.182510	+	0.983204i	$0.558422\pi$
$558$	3.73668	−	32.6557i	0.158186	−	1.38243i
$559$			31.0729i			1.31424i
$560$	−0.0429156	−	0.968808i	−0.00181352	−	0.0409396i
$561$	−4.76710	+	1.66345i	−0.201267	+	0.0702310i
$562$	22.6721	−	22.6721i	0.956363	−	0.956363i
$563$	1.06006	−	1.06006i	0.0446761	−	0.0446761i	−0.684416	−	0.729092i	$-0.739943\pi$
$563$	1.06006	−	1.06006i	0.0446761	−	0.0446761i	0.729092	+	0.684416i	$0.239943\pi$
$564$	9.75992	−	3.40566i	0.410967	−	0.143404i
$565$	−1.65455	−	37.3511i	−0.0696076	−	1.57137i
$566$			12.2396i			0.514467i
$567$	2.06517	+	3.31210i	0.0867291	+	0.139095i
$568$	−9.18067	−	9.18067i	−0.385212	−	0.385212i
$569$	5.21442			0.218600			0.109300	−	0.994009i	$-0.465139\pi$
$569$	5.21442			0.218600			0.109300	+	0.994009i	$0.465139\pi$
$570$	1.52744	−	3.55906i	0.0639773	−	0.149073i
$571$	27.0533			1.13215			0.566073	−	0.824355i	$-0.308462\pi$
$571$	27.0533			1.13215			0.566073	+	0.824355i	$0.308462\pi$
$572$	4.58958	+	4.58958i	0.191900	+	0.191900i
$573$	2.42404	−	5.02244i	0.101266	−	0.209816i
$574$		−	2.63914i		−	0.110155i
$575$	27.1245	+	22.7015i	1.13117	+	0.946717i
$576$	2.34873	−	1.86641i	0.0978637	−	0.0777669i
$577$	−31.9330	+	31.9330i	−1.32939	+	1.32939i	−0.423484	+	0.905903i	$0.639193\pi$
$577$	−31.9330	+	31.9330i	−1.32939	+	1.32939i	−0.905903	+	0.423484i	$0.860807\pi$
$578$	5.28172	−	5.28172i	0.219691	−	0.219691i
$579$	7.23419	+	20.7317i	0.300642	+	0.861578i
$580$	−2.93375	−	2.68486i	−0.121817	−	0.111483i
$581$			4.81344i			0.199695i
$582$	1.59487	+	0.769752i	0.0661096	+	0.0319072i
$583$	4.79897	+	4.79897i	0.198753	+	0.198753i
$584$	−3.58877			−0.148504
$585$	30.2570	+	34.7962i	1.25097	+	1.43864i
$586$	10.1766			0.420392
$587$	−4.54157	−	4.54157i	−0.187450	−	0.187450i	0.607142	−	0.794593i	$-0.292316\pi$
$587$	−4.54157	−	4.54157i	−0.187450	−	0.187450i	−0.794593	+	0.607142i	$0.792316\pi$
$588$	10.6257	+	5.12841i	0.438197	+	0.211492i
$589$			10.9563i			0.451445i
$590$	16.8187	−	0.745024i	0.692415	−	0.0306722i
$591$	5.13351	+	14.7116i	0.211164	+	0.605153i
$592$	3.09818	−	3.09818i	0.127334	−	0.127334i
$593$	−6.70785	+	6.70785i	−0.275458	+	0.275458i	−0.831293	−	0.555835i	$-0.812399\pi$
$593$	−6.70785	+	6.70785i	−0.275458	+	0.275458i	0.555835	+	0.831293i	$0.312399\pi$
$594$	4.14762	+	2.62117i	0.170179	+	0.107548i
$595$	2.02117	−	2.20854i	0.0828601	−	0.0905413i
$596$		−	12.9585i		−	0.530799i
$597$	16.2054	−	33.5765i	0.663243	−	1.37419i
$598$	34.3844	+	34.3844i	1.40608	+	1.40608i
$599$	25.3428			1.03548			0.517740	−	0.855538i	$-0.326774\pi$
$599$	25.3428			1.03548			0.517740	+	0.855538i	$0.326774\pi$
$600$	−3.56505	−	7.89243i	−0.145542	−	0.322207i
$601$	10.1452			0.413833			0.206916	−	0.978359i	$-0.433657\pi$
$601$	10.1452			0.413833			0.206916	+	0.978359i	$0.433657\pi$
$602$	−1.38626	−	1.38626i	−0.0564996	−	0.0564996i
$603$	32.2486	+	3.69010i	1.31327	+	0.150272i
$604$			4.35166i			0.177067i
$605$	−15.2598	+	16.6744i	−0.620400	+	0.677912i
$606$	−2.71164	+	0.946209i	−0.110153	+	0.0384371i
$607$	16.7036	−	16.7036i	0.677979	−	0.677979i	−0.281564	−	0.959543i	$-0.590853\pi$
$607$	16.7036	−	16.7036i	0.677979	−	0.677979i	0.959543	+	0.281564i	$0.0908530\pi$
$608$	−0.707107	+	0.707107i	−0.0286770	+	0.0286770i
$609$	−1.26137	+	0.440148i	−0.0511134	+	0.0178357i
$610$	−10.1304	+	0.448749i	−0.410167	+	0.0181693i
$611$		−	41.0240i		−	1.65965i
$612$	9.20142	+	1.05289i	0.371945	+	0.0425604i
$613$	22.7706	+	22.7706i	0.919695	+	0.919695i	0.997007	−	0.0773118i	$-0.0246337\pi$
$613$	22.7706	+	22.7706i	0.919695	+	0.919695i	−0.0773118	+	0.997007i	$0.524634\pi$
$614$	−2.27946			−0.0919916
$615$	−8.74203	−	21.8871i	−0.352513	−	0.882572i
$616$	−0.409510			−0.0164996
$617$	6.58274	+	6.58274i	0.265011	+	0.265011i	0.827086	−	0.562075i	$-0.189997\pi$
$617$	6.58274	+	6.58274i	0.265011	+	0.265011i	−0.562075	+	0.827086i	$0.689997\pi$
$618$	−1.80219	+	3.73402i	−0.0724948	+	0.150204i
$619$		−	27.5771i		−	1.10842i	−0.832378	−	0.554209i	$-0.813021\pi$
$619$		−	27.5771i		−	1.10842i	0.832378	−	0.554209i	$-0.186979\pi$
$620$	18.0730	+	16.5398i	0.725830	+	0.664253i
$621$	31.0733	+	19.6374i	1.24693	+	0.788022i
$622$	17.0907	−	17.0907i	0.685273	−	0.685273i
$623$	2.72488	−	2.72488i	0.109170	−	0.109170i
$624$	−3.92254	−	11.2412i	−0.157027	−	0.450008i
$625$	−24.6091	+	4.40374i	−0.984363	+	0.176150i
$626$		−	29.0380i		−	1.16059i
$627$	−1.47291	−	0.710886i	−0.0588222	−	0.0283900i
$628$	−5.26086	−	5.26086i	−0.209931	−	0.209931i
$629$	13.5263			0.539330
$630$	−2.90222	−	0.202504i	−0.115627	−	0.00806794i
$631$	−30.6726			−1.22106			−0.610529	−	0.791994i	$-0.709043\pi$
$631$	−30.6726			−1.22106			−0.610529	+	0.791994i	$0.709043\pi$
$632$	−6.71962	−	6.71962i	−0.267292	−	0.267292i
$633$	1.61300	+	0.778502i	0.0641111	+	0.0309427i
$634$			25.9030i			1.02874i
$635$	0.199750	+	4.50930i	0.00792684	+	0.178946i
$636$	−4.10150	−	11.7540i	−0.162635	−	0.466078i
$637$	33.1098	−	33.1098i	1.31186	−	1.31186i
$638$	−1.18748	+	1.18748i	−0.0470127	+	0.0470127i
$639$	−30.4946	+	24.2324i	−1.20635	+	0.958617i
$640$	0.0989549	+	2.23388i	0.00391153	+	0.0883018i
$641$		−	49.7149i		−	1.96362i	−0.189862	−	0.981811i	$-0.560804\pi$
$641$		−	49.7149i		−	1.96362i	0.189862	−	0.981811i	$-0.439196\pi$
$642$	−7.90835	+	16.3856i	−0.312118	+	0.646686i
$643$	−2.40899	−	2.40899i	−0.0950012	−	0.0950012i	0.658009	−	0.753010i	$-0.271399\pi$
$643$	−2.40899	−	2.40899i	−0.0950012	−	0.0950012i	−0.753010	+	0.658009i	$0.771399\pi$
$644$	−3.06798			−0.120896
$645$	−16.0885	−	6.90468i	−0.633485	−	0.271872i
$646$	−3.08715			−0.121462
$647$	5.87644	+	5.87644i	0.231027	+	0.231027i	0.813121	−	0.582094i	$-0.197767\pi$
$647$	5.87644	+	5.87644i	0.231027	+	0.231027i	−0.582094	+	0.813121i	$0.697767\pi$
$648$	−4.76187	−	7.63705i	−0.187064	−	0.300012i
$649$		−	7.10918i		−	0.279060i
$650$	−34.2348	+	3.03898i	−1.34280	+	0.119199i
$651$	7.77054	−	2.71148i	0.304551	−	0.106271i
$652$	2.53089	−	2.53089i	0.0991172	−	0.0991172i
$653$	6.59638	−	6.59638i	0.258136	−	0.258136i	−0.566159	−	0.824296i	$-0.691571\pi$
$653$	6.59638	−	6.59638i	0.258136	−	0.258136i	0.824296	+	0.566159i	$0.191571\pi$
$654$	−12.2518	+	4.27519i	−0.479084	+	0.167173i
$655$	−30.5955	−	27.9999i	−1.19547	−	1.09405i
$656$			6.08532i			0.237592i
$657$	−1.22396	+	10.6965i	−0.0477514	+	0.417311i
$658$	1.83020	+	1.83020i	0.0713487	+	0.0713487i
$659$	−26.7046			−1.04026			−0.520132	−	0.854086i	$-0.674117\pi$
$659$	−26.7046			−1.04026			−0.520132	+	0.854086i	$0.674117\pi$
$660$	−3.39618	+	1.35648i	−0.132196	+	0.0528010i
$661$	−20.8028			−0.809135			−0.404568	−	0.914508i	$-0.632578\pi$
$661$	−20.8028			−0.809135			−0.404568	+	0.914508i	$0.632578\pi$
$662$	11.7123	+	11.7123i	0.455212	+	0.455212i
$663$	15.9762	−	33.1016i	0.620465	−	1.28556i
$664$		−	11.0988i		−	0.430718i
$665$	0.968808	−	0.0429156i	0.0375688	−	0.00166420i
$666$	−8.17764	−	10.2909i	−0.316877	−	0.398766i
$667$	−8.89640	+	8.89640i	−0.344470	+	0.344470i
$668$	−3.33084	+	3.33084i	−0.128874	+	0.128874i
$669$	3.48633	+	9.99110i	0.134789	+	0.386278i
$670$	−16.3336	+	17.8477i	−0.631022	+	0.689518i
$671$			4.28205i			0.165307i
$672$	0.676500	+	0.326507i	0.0260965	+	0.0125953i
$673$	29.5002	+	29.5002i	1.13715	+	1.13715i	0.988959	+	0.148188i	$0.0473442\pi$
$673$	29.5002	+	29.5002i	1.13715	+	1.13715i	0.148188	+	0.988959i	$0.452656\pi$
$674$	35.9137			1.38334
$675$	−24.7397	+	7.93405i	−0.952230	+	0.305382i
$676$	−34.2502			−1.31732
$677$	−35.0885	−	35.0885i	−1.34856	−	1.34856i	−0.887228	−	0.461331i	$-0.847372\pi$
$677$	−35.0885	−	35.0885i	−1.34856	−	1.34856i	−0.461331	−	0.887228i	$-0.652628\pi$
$678$	26.0815	+	12.5880i	1.00165	+	0.483440i
$679$			0.443420i			0.0170169i
$680$	−4.66042	+	5.09245i	−0.178719	+	0.195287i
$681$	−7.13009	−	20.4333i	−0.273226	−	0.783008i
$682$	7.31532	−	7.31532i	0.280118	−	0.280118i
$683$	16.7946	−	16.7946i	0.642629	−	0.642629i	−0.308572	−	0.951201i	$-0.599851\pi$
$683$	16.7946	−	16.7946i	0.642629	−	0.642629i	0.951201	+	0.308572i	$0.0998512\pi$
$684$	1.86641	+	2.34873i	0.0713638	+	0.0898059i
$685$	7.02125	−	0.311023i	0.268268	−	0.0118836i
$686$			5.99007i			0.228702i
$687$	−16.3124	+	33.7983i	−0.622358	+	1.28948i
$688$	3.19643	+	3.19643i	0.121863	+	0.121863i
$689$	−49.4059			−1.88221
$690$	−25.4436	+	10.1626i	−0.968622	+	0.386882i
$691$	−30.1709			−1.14776			−0.573878	−	0.818941i	$-0.694562\pi$
$691$	−30.1709			−1.14776			−0.573878	+	0.818941i	$0.694562\pi$
$692$	−9.61343	−	9.61343i	−0.365448	−	0.365448i
$693$	−0.139665	+	1.22056i	−0.00530543	+	0.0463654i
$694$		−	8.03838i		−	0.305133i
$695$	31.2805	+	28.6267i	1.18654	+	1.08587i
$696$	2.90847	−	1.01489i	0.110245	−	0.0384694i
$697$	−13.2839	+	13.2839i	−0.503165	+	0.503165i
$698$	−12.8335	+	12.8335i	−0.485756	+	0.485756i
$699$	−24.5026	+	8.55003i	−0.926774	+	0.323392i
$700$	1.39174	−	1.66289i	0.0526028	−	0.0628515i
$701$		−	39.5966i		−	1.49554i	−0.663957	−	0.747771i	$-0.731124\pi$
$701$		−	39.5966i		−	1.49554i	0.663957	−	0.747771i	$-0.268876\pi$
$702$	−34.8427	+	7.85749i	−1.31505	+	0.296562i
$703$	3.09818	+	3.09818i	0.116850	+	0.116850i
$704$	0.944248			0.0355877
$705$	21.2408	+	9.11590i	0.799976	+	0.343325i
$706$	12.5368			0.471829
$707$	−0.508493	−	0.508493i	−0.0191238	−	0.0191238i
$708$	−5.66823	+	11.7442i	−0.213025	+	0.441373i
$709$		−	39.9962i		−	1.50209i	−0.660252	−	0.751044i	$-0.729551\pi$
$709$		−	39.9962i		−	1.50209i	0.660252	−	0.751044i	$-0.270449\pi$
$710$	−1.28477	−	29.0034i	−0.0482167	−	1.08848i
$711$	−22.3199	+	17.7364i	−0.837062	+	0.665167i
$712$	−6.28303	+	6.28303i	−0.235466	+	0.235466i
$713$	54.8052	−	54.8052i	2.05247	−	2.05247i
$714$	0.764016	+	2.18951i	0.0285926	+	0.0819404i
$715$	0.642281	+	14.4993i	0.0240199	+	0.542243i
$716$		−	22.6680i		−	0.847143i
$717$	18.1059	+	8.73865i	0.676176	+	0.326351i
$718$	7.62533	+	7.62533i	0.284575	+	0.284575i
$719$	34.6703			1.29298			0.646491	−	0.762921i	$-0.276236\pi$
$719$	34.6703			1.29298			0.646491	+	0.762921i	$0.276236\pi$
$720$	6.69193	+	0.466933i	0.249394	+	0.0174016i
$721$	−1.03816			−0.0386632
$722$	−0.707107	−	0.707107i	−0.0263158	−	0.0263158i
$723$	−32.2732	−	15.5764i	−1.20025	−	0.579293i
$724$			3.95190i			0.146871i
$725$	−0.786287	−	8.85768i	−0.0292020	−	0.328966i
$726$	−5.76830	−	16.5308i	−0.214082	−	0.613514i
$727$	2.33610	−	2.33610i	0.0866412	−	0.0866412i	−0.662458	−	0.749099i	$-0.730487\pi$
$727$	2.33610	−	2.33610i	0.0866412	−	0.0866412i	0.749099	+	0.662458i	$0.230487\pi$
$728$	2.10797	−	2.10797i	0.0781267	−	0.0781267i
$729$	−24.3867	+	11.5884i	−0.903210	+	0.429198i
$730$	−5.91990	−	5.41767i	−0.219105	−	0.200517i
$731$			13.9553i			0.516155i
$732$	3.41413	−	7.07384i	0.126190	−	0.261457i
$733$	−25.5392	−	25.5392i	−0.943311	−	0.943311i	0.0551665	−	0.998477i	$-0.482431\pi$
$733$	−25.5392	−	25.5392i	−0.943311	−	0.943311i	−0.998477	+	0.0551665i	$0.982431\pi$
$734$	−13.1175			−0.484175
$735$	9.78583	+	24.5004i	0.360956	+	0.903711i
$736$	7.07416			0.260757
$737$	7.22413	+	7.22413i	0.266104	+	0.266104i
$738$	18.1376	+	2.07542i	0.667655	+	0.0763974i
$739$		−	6.43422i		−	0.236686i	−0.992973	−	0.118343i	$-0.962242\pi$
$739$		−	6.43422i		−	0.236686i	0.992973	−	0.118343i	$-0.0377583\pi$
$740$	9.78771	−	0.433570i	0.359803	−	0.0159383i
$741$	11.2412	−	3.92254i	0.412955	−	0.144098i
$742$	2.20414	−	2.20414i	0.0809167	−	0.0809167i
$743$	2.23501	−	2.23501i	0.0819944	−	0.0819944i	−0.664920	−	0.746915i	$-0.731534\pi$
$743$	2.23501	−	2.23501i	0.0819944	−	0.0819944i	0.746915	+	0.664920i	$0.231534\pi$
$744$	−17.9173	+	6.25213i	−0.656880	+	0.229214i
$745$	19.5623	−	21.3758i	0.716708	−	0.783148i
$746$		−	6.60357i		−	0.241774i
$747$	−33.0806	−	3.78530i	−1.21036	−	0.138497i
$748$	2.06124	+	2.06124i	0.0753665	+	0.0753665i
$749$	−4.55565			−0.166460
$750$	6.03379	−	18.4009i	0.220323	−	0.671906i
$751$	−33.0311			−1.20532			−0.602660	−	0.797998i	$-0.705893\pi$
$751$	−33.0311			−1.20532			−0.602660	+	0.797998i	$0.705893\pi$
$752$	−4.22008	−	4.22008i	−0.153891	−	0.153891i
$753$	−11.7144	+	24.2714i	−0.426895	+	0.884498i
$754$		−	12.2252i		−	0.445216i
$755$	−6.56935	+	7.17833i	−0.239083	+	0.261246i
$756$	1.20389	−	1.90498i	0.0437852	−	0.0692836i
$757$	−22.2750	+	22.2750i	−0.809598	+	0.809598i	−0.984573	−	0.174975i	$-0.944016\pi$
$757$	−22.2750	+	22.2750i	−0.809598	+	0.809598i	0.174975	+	0.984573i	$0.444016\pi$
$758$	−15.2909	+	15.2909i	−0.555390	+	0.555390i
$759$	3.81177	+	10.9237i	0.138358	+	0.396506i
$760$	−2.23388	+	0.0989549i	−0.0810312	+	0.00358947i
$761$		−	19.7060i		−	0.714342i	−0.934039	−	0.357171i	$-0.883741\pi$
$761$		−	19.7060i		−	0.714342i	0.934039	−	0.357171i	$-0.116259\pi$
$762$	−3.14876	−	1.51972i	−0.114067	−	0.0550537i
$763$	−2.29749	−	2.29749i	−0.0831746	−	0.0831746i
$764$	−3.21978			−0.116487
$765$	13.5889	+	15.6274i	0.491306	+	0.565011i
$766$	−28.0358			−1.01297
$767$	36.5949	+	36.5949i	1.32136	+	1.32136i
$768$	−1.55987	−	0.752859i	−0.0562871	−	0.0271665i
$769$			1.48367i			0.0535024i	0.999642	+	0.0267512i	$0.00851619\pi$
$769$			1.48367i			0.0535024i	−0.999642	+	0.0267512i	$0.991484\pi$
$770$	−0.675512	−	0.618203i	−0.0243437	−	0.0222785i
$771$	−2.40953	−	6.90521i	−0.0867771	−	0.248685i
$772$	8.96414	−	8.96414i	0.322627	−	0.322627i
$773$	−9.99213	+	9.99213i	−0.359392	+	0.359392i	−0.863589	−	0.504197i	$-0.831789\pi$
$773$	−9.99213	+	9.99213i	−0.359392	+	0.359392i	0.504197	+	0.863589i	$0.331789\pi$
$774$	10.6173	−	8.43697i	0.381630	−	0.303260i
$775$	4.84383	+	54.5667i	0.173995	+	1.96009i
$776$		−	1.02244i		−	0.0367034i
$777$	1.43059	−	2.96408i	0.0513220	−	0.106336i
$778$	−12.7505	−	12.7505i	−0.457129	−	0.457129i
$779$	−6.08532			−0.218029
$780$	10.4994	−	24.4646i	0.375940	−	0.875972i
$781$	−12.2596			−0.438682
$782$	15.4425	+	15.4425i	0.552223	+	0.552223i
$783$	−2.03299	−	9.01498i	−0.0726533	−	0.322169i
$784$		−	6.81191i		−	0.243283i
$785$	−0.736223	−	16.6200i	−0.0262769	−	0.593194i
$786$	30.3319	−	10.5841i	1.08190	−	0.377523i
$787$	1.19902	−	1.19902i	0.0427405	−	0.0427405i	−0.685414	−	0.728154i	$-0.740379\pi$
$787$	1.19902	−	1.19902i	0.0427405	−	0.0427405i	0.728154	+	0.685414i	$0.240379\pi$
$788$	6.36112	−	6.36112i	0.226605	−	0.226605i
$789$	19.7901	−	6.90563i	0.704546	−	0.245847i
$790$	−0.940365	−	21.2285i	−0.0334567	−	0.755275i
$791$			7.25141i			0.257830i
$792$	0.322039	−	2.81438i	0.0114432	−	0.100005i
$793$	−22.0421	−	22.0421i	−0.782739	−	0.782739i
$794$	−21.4001			−0.759462
$795$	10.9784	−	25.5807i	0.389365	−	0.907254i
$796$	−21.5251			−0.762938
$797$	18.6007	+	18.6007i	0.658871	+	0.658871i	0.955113	−	0.296242i	$-0.0957335\pi$
$797$	18.6007	+	18.6007i	0.658871	+	0.658871i	−0.296242	+	0.955113i	$0.595734\pi$
$798$	−0.326507	+	0.676500i	−0.0115582	+	0.0239478i
$799$		−	18.4244i		−	0.651810i
$800$	−3.20907	+	3.83430i	−0.113458	+	0.135563i
$801$	16.5840	+	20.8697i	0.585968	+	0.737396i
$802$	7.16366	−	7.16366i	0.252958	−	0.252958i
$803$	−2.39616	+	2.39616i	−0.0845588	+	0.0845588i
$804$	−6.17419	−	17.6940i	−0.217747	−	0.624018i
$805$	−5.06083	−	4.63149i	−0.178371	−	0.163238i
$806$			75.3120i			2.65275i
$807$	17.2131	+	8.30778i	0.605931	+	0.292448i
$808$	1.17248	+	1.17248i	0.0412478	+	0.0412478i
$809$	−29.5206			−1.03789			−0.518945	−	0.854808i	$-0.673675\pi$
$809$	−29.5206			−1.03789			−0.518945	+	0.854808i	$0.673675\pi$
$810$	3.67403	−	19.7864i	0.129092	−	0.695223i
$811$	−19.0909			−0.670373			−0.335186	−	0.942152i	$-0.608799\pi$
$811$	−19.0909			−0.670373			−0.335186	+	0.942152i	$0.608799\pi$
$812$	0.545404	+	0.545404i	0.0191399	+	0.0191399i
$813$	19.0071	+	9.17363i	0.666610	+	0.321733i
$814$		−	4.13721i		−	0.145009i
$815$	7.99553	−	0.354181i	0.280071	−	0.0124064i
$816$	−1.76167	−	5.04857i	−0.0616707	−	0.176735i
$817$	−3.19643	+	3.19643i	−0.111829	+	0.111829i
$818$	−6.31543	+	6.31543i	−0.220814	+	0.220814i
$819$	−5.56399	−	7.00186i	−0.194422	−	0.244665i
$820$	−9.18652	+	10.0381i	−0.320807	+	0.350546i
$821$			36.9019i			1.28789i	0.765074	+	0.643943i	$0.222703\pi$
$821$			36.9019i			1.28789i	−0.765074	+	0.643943i	$0.777297\pi$
$822$	−2.36630	+	4.90280i	−0.0825341	+	0.171005i
$823$	−1.58603	−	1.58603i	−0.0552855	−	0.0552855i	0.678924	−	0.734209i	$-0.262447\pi$
$823$	−1.58603	−	1.58603i	−0.0552855	−	0.0552855i	−0.734209	+	0.678924i	$0.762447\pi$
$824$	2.39380			0.0833918
$825$	−7.64997	−	2.88932i	−0.266338	−	0.100593i
$826$	−3.26521			−0.113611
$827$	−14.6947	−	14.6947i	−0.510984	−	0.510984i	0.403844	−	0.914828i	$-0.367674\pi$
$827$	−14.6947	−	14.6947i	−0.510984	−	0.510984i	−0.914828	+	0.403844i	$0.867674\pi$
$828$	2.41267	−	21.0849i	0.0838461	−	0.732751i
$829$		−	7.51933i		−	0.261157i	−0.991438	−	0.130579i	$-0.958316\pi$
$829$		−	7.51933i		−	0.261157i	0.991438	−	0.130579i	$-0.0416835\pi$
$830$	16.7550	−	18.3082i	0.581575	−	0.635487i
$831$	−11.1212	+	3.88066i	−0.385789	+	0.134619i
$832$	−4.86057	+	4.86057i	−0.168510	+	0.168510i
$833$	14.8701	−	14.8701i	0.515217	−	0.515217i
$834$	−31.0110	+	10.8211i	−1.07382	+	0.374703i
$835$	−10.5227	+	0.466130i	−0.364154	+	0.0161311i
$836$			0.944248i			0.0326575i
$837$	12.5240	+	55.5357i	0.432894	+	1.91960i
$838$	−14.5706	−	14.5706i	−0.503333	−	0.503333i
$839$	5.59026			0.192997			0.0964985	−	0.995333i	$-0.469236\pi$
$839$	5.59026			0.192997			0.0964985	+	0.995333i	$0.469236\pi$
$840$	0.623027	+	1.55985i	0.0214965	+	0.0538199i
$841$	−25.8369			−0.890929
$842$	10.6801	+	10.6801i	0.368060	+	0.368060i
$843$	−24.1390	+	50.0144i	−0.831392	+	1.72259i
$844$		−	1.03406i		−	0.0355938i
$845$	−56.4979	−	51.7048i	−1.94359	−	1.77870i
$846$	−14.0174	+	11.1389i	−0.481930	+	0.382963i
$847$	3.09989	−	3.09989i	0.106513	−	0.106513i
$848$	−5.08232	+	5.08232i	−0.174527	+	0.174527i
$849$	−6.98445	−	20.0160i	−0.239706	−	0.686946i
$850$	−15.3753	+	1.36485i	−0.527369	+	0.0468140i
$851$		−	30.9954i		−	1.06251i
$852$	20.2525	+	9.77470i	0.693839	+	0.334876i
$853$	12.5659	+	12.5659i	0.430247	+	0.430247i	0.888712	−	0.458465i	$-0.151601\pi$
$853$	12.5659	+	12.5659i	0.430247	+	0.430247i	−0.458465	+	0.888712i	$0.651601\pi$
$854$	1.96673			0.0673001
$855$	−0.466933	+	6.69193i	−0.0159688	+	0.228859i
$856$	10.5044			0.359034
$857$	−20.9298	−	20.9298i	−0.714948	−	0.714948i	0.252618	−	0.967566i	$-0.418708\pi$
$857$	−20.9298	−	20.9298i	−0.714948	−	0.714948i	−0.967566	+	0.252618i	$0.918708\pi$
$858$	−10.1246	−	4.88654i	−0.345648	−	0.166824i
$859$		−	32.5560i		−	1.11080i	−0.831585	−	0.555398i	$-0.812566\pi$
$859$		−	32.5560i		−	1.11080i	0.831585	−	0.555398i	$-0.187434\pi$
$860$	0.447319	+	10.0981i	0.0152535	+	0.344342i
$861$	1.50601	+	4.31591i	0.0513247	+	0.147086i
$862$	5.22885	−	5.22885i	0.178095	−	0.178095i
$863$	29.9371	−	29.9371i	1.01907	−	1.01907i	0.0192563	−	0.999815i	$-0.493870\pi$
$863$	29.9371	−	29.9371i	1.01907	−	1.01907i	0.999815	−	0.0192563i	$-0.00612986\pi$
$864$	−2.77594	+	4.39251i	−0.0944393	+	0.149436i
$865$	−1.34534	−	30.3706i	−0.0457428	−	1.03263i
$866$		−	9.22376i		−	0.313436i
$867$	−5.62347	+	11.6514i	−0.190983	+	0.395704i
$868$	−3.35989	−	3.35989i	−0.114042	−	0.114042i
$869$	−8.97316			−0.304394
$870$	6.32981	+	2.71655i	0.214600	+	0.0920998i
$871$	−74.3732			−2.52004
$872$	5.29755	+	5.29755i	0.179398	+	0.179398i
$873$	−3.04743	−	0.348706i	−0.103140	−	0.0118019i
$874$			7.07416i			0.239287i
$875$	4.80609	−	0.642054i	0.162476	−	0.0217054i
$876$	5.86889	−	2.04791i	0.198291	−	0.0691926i
$877$	−1.12380	+	1.12380i	−0.0379481	+	0.0379481i	−0.725826	−	0.687878i	$-0.758542\pi$
$877$	−1.12380	+	1.12380i	−0.0379481	+	0.0379481i	0.687878	+	0.725826i	$0.258542\pi$
$878$	22.6865	−	22.6865i	0.765632	−	0.765632i
$879$	−16.6423	+	5.80723i	−0.561331	+	0.195873i
$880$	1.55759	+	1.42545i	0.0525065	+	0.0480520i
$881$			52.9484i			1.78388i	0.452158	+	0.891938i	$0.350654\pi$
$881$			52.9484i			1.78388i	−0.452158	+	0.891938i	$0.649346\pi$
$882$	−20.3033	−	2.32323i	−0.683646	−	0.0782272i
$883$	−15.4219	−	15.4219i	−0.518989	−	0.518989i	0.398276	−	0.917266i	$-0.369609\pi$
$883$	−15.4219	−	15.4219i	−0.518989	−	0.518989i	−0.917266	+	0.398276i	$0.869609\pi$
$884$	−21.2207			−0.713730
$885$	−27.0793	+	10.8159i	−0.910261	+	0.363572i
$886$	−7.87370			−0.264522
$887$	14.7809	+	14.7809i	0.496293	+	0.496293i	0.910282	−	0.413989i	$-0.135865\pi$
$887$	14.7809	+	14.7809i	0.496293	+	0.496293i	−0.413989	+	0.910282i	$0.635865\pi$
$888$	−3.29864	+	6.83457i	−0.110695	+	0.229353i
$889$		−	0.875444i		−	0.0293614i
$890$	−19.8492	+	0.879268i	−0.665347	+	0.0294731i
$891$	−8.27856	−	1.91971i	−0.277342	−	0.0643127i
$892$	4.32004	−	4.32004i	0.144646	−	0.144646i
$893$	4.22008	−	4.22008i	0.141220	−	0.141220i
$894$	7.39468	+	21.1916i	0.247315	+	0.708753i
$895$	34.2200	−	37.3923i	1.14385	−	1.24989i
$896$		−	0.433689i		−	0.0144885i
$897$	−75.8518	−	36.6092i	−2.53262	−	1.22235i
$898$	−15.6572	−	15.6572i	−0.522487	−	0.522487i
$899$	−19.4857			−0.649886
$900$	10.3339	+	10.8725i	0.344462	+	0.362417i
$901$	−22.1889			−0.739218
$902$	4.06307	+	4.06307i	0.135286	+	0.135286i
$903$	3.05807	+	1.47595i	0.101766	+	0.0491166i
$904$		−	16.7203i		−	0.556109i
$905$	−5.96587	+	6.51891i	−0.198312	+	0.216696i
$906$	−2.48325	−	7.11648i	−0.0825006	−	0.236429i
$907$	−22.2347	+	22.2347i	−0.738290	+	0.738290i	−0.972247	−	0.233957i	$-0.924833\pi$
$907$	−22.2347	+	22.2347i	−0.738290	+	0.738290i	0.233957	+	0.972247i	$0.424833\pi$
$908$	−8.83516	+	8.83516i	−0.293205	+	0.293205i
$909$	3.89452	−	3.09476i	0.129173	−	0.102647i
$910$	6.65947	−	0.294997i	0.220759	−	0.00977906i
$911$		−	10.9407i		−	0.362480i	−0.983439	−	0.181240i	$-0.941989\pi$
$911$		−	10.9407i		−	0.362480i	0.983439	−	0.181240i	$-0.0580111\pi$
$912$	0.752859	−	1.55987i	0.0249297	−	0.0516525i
$913$	−7.41051	−	7.41051i	−0.245252	−	0.245252i
$914$	1.79823			0.0594803
$915$	16.3106	−	6.51471i	0.539213	−	0.215370i
$916$	21.6673			0.715908
$917$	5.68791	+	5.68791i	0.187831	+	0.187831i
$918$	−15.6484	+	3.52891i	−0.516473	+	0.116471i
$919$		−	20.3908i		−	0.672632i	−0.941749	−	0.336316i	$-0.890819\pi$
$919$		−	20.3908i		−	0.672632i	0.941749	−	0.336316i	$-0.109181\pi$
$920$	11.6693	+	10.6793i	0.384724	+	0.352085i
$921$	3.72772	−	1.30076i	0.122832	−	0.0428616i
$922$	22.1186	−	22.1186i	0.728439	−	0.728439i
$923$	63.1069	−	63.1069i	2.07719	−	2.07719i
$924$	0.669691	−	0.233685i	0.0220312	−	0.00768766i
$925$	16.8000	+	14.0605i	0.552379	+	0.462307i
$926$			17.4078i			0.572056i
$927$	0.816414	−	7.13483i	0.0268145	−	0.234339i
$928$	−1.25759	−	1.25759i	−0.0412825	−	0.0412825i
$929$	7.33339			0.240601			0.120300	−	0.992738i	$-0.461614\pi$
$929$	7.33339			0.240601			0.120300	+	0.992738i	$0.461614\pi$
$930$	−38.9940	−	16.7350i	−1.27866	−	0.548763i
$931$	6.81191			0.223251
$932$	10.5947	+	10.5947i	0.347040	+	0.347040i
$933$	−18.1965	+	37.7019i	−0.595726	+	1.23430i
$934$			4.36576i			0.142852i
$935$	0.288457	+	6.51184i	0.00943356	+	0.212960i
$936$	12.8295	+	16.1449i	0.419344	+	0.527712i
$937$	16.6534	−	16.6534i	0.544044	−	0.544044i	−0.380668	−	0.924712i	$-0.624306\pi$
$937$	16.6534	−	16.6534i	0.544044	−	0.544044i	0.924712	+	0.380668i	$0.124306\pi$
$938$	3.31801	−	3.31801i	0.108337	−	0.108337i
$939$	16.5704	+	47.4872i	0.540754	+	1.54969i
$940$	−0.590572	−	13.3320i	−0.0192623	−	0.434842i
$941$			41.0823i			1.33924i	0.742702	+	0.669622i	$0.233544\pi$
$941$			41.0823i			1.33924i	−0.742702	+	0.669622i	$0.766456\pi$
$942$	11.6054	+	5.60126i	0.378125	+	0.182499i
$943$	30.4399	+	30.4399i	0.991260	+	0.991260i
$944$	7.52893			0.245046
$945$	4.86169	−	1.32497i	0.158151	−	0.0431013i
$946$	4.26841			0.138778
$947$	43.3537	+	43.3537i	1.40880	+	1.40880i	0.766186	+	0.642619i	$0.222152\pi$
$947$	43.3537	+	43.3537i	1.40880	+	1.40880i	0.642619	+	0.766186i	$0.277848\pi$
$948$	14.8234	+	7.15440i	0.481443	+	0.232364i
$949$		−	24.6688i		−	0.800782i
$950$	−3.83430	−	3.20907i	−0.124401	−	0.104116i
$951$	−14.7814	−	42.3605i	−0.479321	−	1.37363i
$952$	0.946720	−	0.946720i	0.0306834	−	0.0306834i
$953$	−33.0634	+	33.0634i	−1.07103	+	1.07103i	−0.0737523	+	0.997277i	$0.523497\pi$
$953$	−33.0634	+	33.0634i	−1.07103	+	1.07103i	−0.997277	+	0.0737523i	$0.976503\pi$
$954$	13.4148	+	16.8814i	0.434319	+	0.546557i
$955$	−5.31122	−	4.86063i	−0.171867	−	0.157286i
$956$		−	11.6073i		−	0.375406i
$957$	1.26431	−	2.61957i	0.0408694	−	0.0846786i
$958$	2.22678	+	2.22678i	0.0719441	+	0.0719441i
$959$	−1.36312			−0.0440174
$960$	−1.43658	−	3.59670i	−0.0463653	−	0.116083i
$961$	89.0396			2.87225
$962$	21.2965	+	21.2965i	0.686628	+	0.686628i
$963$	3.58257	−	31.3090i	0.115447	−	1.00892i
$964$			20.6897i			0.666369i
$965$	28.3193	−	1.25447i	0.911632	−	0.0403829i
$966$	5.01722	−	1.75073i	0.161427	−	0.0563288i
$967$	−8.96271	+	8.96271i	−0.288221	+	0.288221i	−0.836377	−	0.548155i	$-0.815330\pi$
$967$	−8.96271	+	8.96271i	−0.288221	+	0.288221i	0.548155	+	0.836377i	$0.315330\pi$
$968$	−7.14772	+	7.14772i	−0.229736	+	0.229736i
$969$	5.04857	−	1.76167i	0.162184	−	0.0565929i
$970$	1.54349	−	1.68657i	0.0495585	−	0.0541526i
$971$		−	56.8504i		−	1.82442i	−0.409726	−	0.912209i	$-0.634376\pi$
$971$		−	56.8504i		−	1.82442i	0.409726	−	0.912209i	$-0.365624\pi$
$972$	12.1454	+	9.77190i	0.389563	+	0.313434i
$973$	−5.81525	−	5.81525i	−0.186428	−	0.186428i
$974$	−20.2091			−0.647541
$975$	54.2516	−	24.5057i	1.73744	−	0.784811i
$976$	−4.53489			−0.145158
$977$	−20.1899	−	20.1899i	−0.645933	−	0.645933i	0.306074	−	0.952008i	$-0.400984\pi$
$977$	−20.1899	−	20.1899i	−0.645933	−	0.645933i	−0.952008	+	0.306074i	$0.900984\pi$
$978$	−2.69464	+	5.58312i	−0.0861652	+	0.178528i
$979$			8.39015i			0.268150i
$980$	10.2834	−	11.2367i	0.328491	−	0.358942i
$981$	17.5964	−	13.9829i	0.561808	−	0.446438i
$982$	−2.51893	+	2.51893i	−0.0803823	+	0.0803823i
$983$	−12.2333	+	12.2333i	−0.390180	+	0.390180i	−0.874752	−	0.484571i	$-0.838976\pi$
$983$	−12.2333	+	12.2333i	−0.390180	+	0.390180i	0.484571	+	0.874752i	$0.338976\pi$
$984$	−3.47256	−	9.95162i	−0.110701	−	0.317246i
$985$	20.0959	−	0.890196i	0.640309	−	0.0283640i
$986$		−	5.49051i		−	0.174854i
$987$	−4.03741	−	1.94862i	−0.128512	−	0.0620254i
$988$	−4.86057	−	4.86057i	−0.154635	−	0.154635i
$989$	31.9783			1.01685
$990$	4.77986	−	4.15633i	0.151914	−	0.132097i
$991$	25.1249			0.798118			0.399059	−	0.916925i	$-0.369337\pi$
$991$	25.1249			0.798118			0.399059	+	0.916925i	$0.369337\pi$
$992$	7.74725	+	7.74725i	0.245975	+	0.245975i
$993$	−25.8373	−	12.4701i	−0.819921	−	0.395728i
$994$			5.63077i			0.178597i
$995$	−35.5070	−	32.4947i	−1.12565	−	1.03015i
$996$	6.33349	+	18.1505i	0.200684	+	0.575119i
$997$	−28.2711	+	28.2711i	−0.895354	+	0.895354i	−0.995021	−	0.0996671i	$-0.968222\pi$
$997$	−28.2711	+	28.2711i	−0.895354	+	0.895354i	0.0996671	+	0.995021i	$0.468222\pi$
$998$	−16.1168	+	16.1168i	−0.510170	+	0.510170i
$999$	19.2458	+	12.1627i	0.608909	+	0.384812i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.k.a.533.10	yes	36
3.2	odd	2	inner	570.2.k.a.533.4	yes	36
5.2	odd	4	inner	570.2.k.a.77.4	✓	36
15.2	even	4	inner	570.2.k.a.77.10	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.k.a.77.4	✓	36	5.2	odd	4	inner
570.2.k.a.77.10	yes	36	15.2	even	4	inner
570.2.k.a.533.4	yes	36	3.2	odd	2	inner
570.2.k.a.533.10	yes	36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.55987 - 0.752859i) q^{3} +1.00000i q^{4} +(-1.50962 + 1.64956i) q^{5} +(-0.570645 - 1.63535i) q^{6} +(0.306664 - 0.306664i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.86641 + 2.34873i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.55987 - 0.752859i) q^{3} +1.00000i q^{4} +(-1.50962 + 1.64956i) q^{5} +(-0.570645 - 1.63535i) q^{6} +(0.306664 - 0.306664i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.86641 + 2.34873i) q^{9} +(-2.23388 + 0.0989549i) q^{10} +0.944248i q^{11} +(0.752859 - 1.55987i) q^{12} +(-4.86057 - 4.86057i) q^{13} +0.433689 q^{14} +(3.59670 - 1.43658i) q^{15} -1.00000 q^{16} +(-2.18295 - 2.18295i) q^{17} +(-0.341054 + 2.98055i) q^{18} -1.00000i q^{19} +(-1.64956 - 1.50962i) q^{20} +(-0.709233 + 0.247482i) q^{21} +(-0.667684 + 0.667684i) q^{22} +(-5.00219 + 5.00219i) q^{23} +(1.63535 - 0.570645i) q^{24} +(-0.442106 - 4.98042i) q^{25} -6.87388i q^{26} +(-1.14309 - 5.06886i) q^{27} +(0.306664 + 0.306664i) q^{28} +1.77850 q^{29} +(3.55906 + 1.52744i) q^{30} -10.9563 q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.710886 - 1.47291i) q^{33} -3.08715i q^{34} +(0.0429156 + 0.968808i) q^{35} +(-2.34873 + 1.86641i) q^{36} +(-3.09818 + 3.09818i) q^{37} +(0.707107 - 0.707107i) q^{38} +(3.92254 + 11.2412i) q^{39} +(-0.0989549 - 2.23388i) q^{40} -6.08532i q^{41} +(-0.676500 - 0.326507i) q^{42} +(-3.19643 - 3.19643i) q^{43} -0.944248 q^{44} +(-6.69193 - 0.466933i) q^{45} -7.07416 q^{46} +(4.22008 + 4.22008i) q^{47} +(1.55987 + 0.752859i) q^{48} +6.81191i q^{49} +(3.20907 - 3.83430i) q^{50} +(1.76167 + 5.04857i) q^{51} +(4.86057 - 4.86057i) q^{52} +(5.08232 - 5.08232i) q^{53} +(2.77594 - 4.39251i) q^{54} +(-1.55759 - 1.42545i) q^{55} +0.433689i q^{56} +(-0.752859 + 1.55987i) q^{57} +(1.25759 + 1.25759i) q^{58} -7.52893 q^{59} +(1.43658 + 3.59670i) q^{60} +4.53489 q^{61} +(-7.74725 - 7.74725i) q^{62} +(1.29263 + 0.147911i) q^{63} -1.00000i q^{64} +(15.3554 - 0.680204i) q^{65} +(1.54417 - 0.538830i) q^{66} +(7.65067 - 7.65067i) q^{67} +(2.18295 - 2.18295i) q^{68} +(11.5687 - 4.03683i) q^{69} +(-0.654705 + 0.715397i) q^{70} +12.9834i q^{71} +(-2.98055 - 0.341054i) q^{72} +(2.53764 + 2.53764i) q^{73} -4.38149 q^{74} +(-3.05992 + 8.10166i) q^{75} +1.00000 q^{76} +(0.289567 + 0.289567i) q^{77} +(-5.17507 + 10.7224i) q^{78} +9.50297i q^{79} +(1.50962 - 1.64956i) q^{80} +(-2.03306 + 8.76736i) q^{81} +(4.30297 - 4.30297i) q^{82} +(-7.84806 + 7.84806i) q^{83} +(-0.247482 - 0.709233i) q^{84} +(6.89632 - 0.305489i) q^{85} -4.52043i q^{86} +(-2.77424 - 1.33896i) q^{87} +(-0.667684 - 0.667684i) q^{88} +8.88554 q^{89} +(-4.40174 - 5.06208i) q^{90} -2.98113 q^{91} +(-5.00219 - 5.00219i) q^{92} +(17.0904 + 8.24852i) q^{93} +5.96810i q^{94} +(1.64956 + 1.50962i) q^{95} +(0.570645 + 1.63535i) q^{96} +(-0.722973 + 0.722973i) q^{97} +(-4.81675 + 4.81675i) q^{98} +(-2.21778 + 1.76235i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7}+O(q^{10}) \) 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7	\( 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} - 32 q^{21} - 4 q^{22} + 32 q^{25} + 28 q^{27} - 12 q^{28} - 8 q^{30} + 8 q^{31} + 36 q^{33} + 4 q^{36} - 32 q^{37} - 8 q^{40} + 12 q^{42} - 24 q^{43} - 28 q^{45} - 16 q^{46} - 4 q^{48} - 40 q^{51} - 8 q^{52} - 4 q^{55} + 4 q^{57} - 4 q^{58} - 24 q^{60} + 200 q^{61} + 28 q^{63} + 12 q^{70} - 68 q^{73} - 36 q^{75} + 36 q^{76} + 24 q^{78} - 92 q^{81} + 24 q^{82} + 24 q^{85} + 28 q^{87} - 4 q^{88} - 68 q^{90} + 64 q^{91} + 16 q^{93} - 4 q^{96} - 148 q^{97}+O(q^{100}) \) 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7 - 4 * q^10 - 4 * q^12 + 8 * q^13 + 4 * q^15 - 36 * q^16 - 32 * q^21 - 4 * q^22 + 32 * q^25 + 28 * q^27 - 12 * q^28 - 8 * q^30 + 8 * q^31 + 36 * q^33 + 4 * q^36 - 32 * q^37 - 8 * q^40 + 12 * q^42 - 24 * q^43 - 28 * q^45 - 16 * q^46 - 4 * q^48 - 40 * q^51 - 8 * q^52 - 4 * q^55 + 4 * q^57 - 4 * q^58 - 24 * q^60 + 200 * q^61 + 28 * q^63 + 12 * q^70 - 68 * q^73 - 36 * q^75 + 36 * q^76 + 24 * q^78 - 92 * q^81 + 24 * q^82 + 24 * q^85 + 28 * q^87 - 4 * q^88 - 68 * q^90 + 64 * q^91 + 16 * q^93 - 4 * q^96 - 148 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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